TL; DR When a ratfolk has a tailblade, a manufactured weapon, strapped to its tail and makes a full attack—either with only natural weapons (including the tail attack granted by the tailblade) or with only traditional weapons (including the tailblade used like a normal weapon) or with both—, all attacks incorporating the tailblade (i.e. the tail attack and normal attacks) are considered secondary attacks. The tailblade in its originally presentation, though, is vague, and I don't think Paizo ever revisited it, so the GM must make some rulings.
You're correct that the tailblade is ambiguous
The tailblade (Advanced Race Guide 154) (11 gp; 0.5 lbs.) appears in the section Ratfolk Equipment (153–4), and as the only entry on Table 2–3: Ratfolk Weapons (154). Its original description doesn't look like this, though, but like this:
A tailblade is a small, sharp knife designed to be strapped to the tip of a wielder’s tail. It takes a full-round action to strap on or remove a tailblade. The wearer can loosely attach the tailblade (without strapping it securely in place) as a move action, but using a loosely attached tailblade gives the wielder a –4 penalty on all attack rolls made with the weapon, and other creatures get a +4 bonus on disarm combat maneuver checks to disarm the tailblade. A ratfolk wielding a tailblade can make a tail attack, adding its Strength modifier to the tailblade’s damage. Ratfolk are considered proficient with such attacks and can apply feats or effects appropriate to natural attacks to tail attacks made with a tailblade. If used as part of a full attack action, attacks with a tailblade are considered secondary attacks. (Link added)
So when it's presented like this—sans all those fancy italics and paragraph breaks—, my instinct is to approach the tailblade like I would any other light martial weapon without a range increment. After all, that's what a tailblade is until the description explains how it's different. Grab some tea, settle in, and let's go.
"A tailblade is a small, sharp knife designed to be strapped to the tip of a wielder’s tail." Thus the tailblade itself literally can't be anything except a manufactured weapon, and a light martial melee weapon, at that. Yes, somebody is sitting at a forge and pounding out these puppies, basic economics be damned. Still: fantasy adventure game—I won't overthink it if you don't.
"It takes a full-round action to strap on or remove a tailblade." And: "The wearer can loosely attach the tailblade…." Many ratfolk will likely have the feat Quick Draw anyway, but if mine didn't then I'd buy pizza one night so the GM would rule that drawing the tailblade is part of the full-round action that's needed to strap on a tailblade. Then, considering the next sentence and overall context, it seems that strapping on the tailblade is the only way that tailblade can be wielded. With that in mind, I'd have these rules completely subsume the normal rules for wielding a weapon when a tailblade is involved.
(To be clear, I personally think verisimilitude suffers if a tailblade can instead be wielded normally like most other weapons—that is, for example, in a ratfolk's paws instead of strapped to his tail—because, then, when the ratfolk make a full attack with the tailblade wielded normally, still the "attacks with a tailblade are considered secondary attacks" but, now, for no apparent reason (see below). Of course, a more generous or imaginative GM could allow normal wielding of a tailblade (i.e. in paws not to tail) and mark that secondary attack language as a unique feature of the tailblade, but I'd feel obligated to dig in and square that ruling with similar weapons without that secondary attack language. That may be just me, though.)
"A ratfolk wielding a tailblade can make a tail attack, adding its Strength modifier to the tailblade’s damage." Intervening sentence omitted (see below) and then: "If used as part of a full attack action, attacks with a tailblade are considered secondary attacks." I have to assume that this tail attack (that's the product of the ratfolk wielding the tailblade by attaching it to his tail) is supposed to follow the rules for a natural attack. (I know that this is a bold assumption, but my alternative readings yield unplayable gibberish.)
With that in mind, what I think may be overlooked is that despite a ratfolk being able to make a tail attack with the tailblade, the tailblade never stops being an otherwise normal light martial melee weapon (albeit wielded by the ratfolk's tail). Thus a ratfolk can make (or can plan to make) that tail attack, yet a ratfolk that does isn't thereby prevented from making attacks with unarmed strikes or other manufactured weapons—including an attached tailblade! Because the tailblade is always a light martial melee weapon, a ratfolk can totally just stab a fool with it without making a tail attack! Wielding a tailblade as indicated doesn't prohibit the weapon from being used as a normal weapon. Hence:
A ratfolk can take a standard action to make a standard attack with either his tail attack (with which he is automatically proficient and that deals damage equal to the appropriate tailblade damage + his Str modifier) or a natural weapon that the ratfolk possesses or the tailblade as if it were just another light martial melee weapon (which, in this case, it is) or another manufactured weapon altogether or an unarmed strike.
(Here I assume that the tail attack is a naturalish attack that's primaryish. What I mean is that no bonuses or penalties from the tail attack being a primary attack seem to apply to the tail attack when a ratfolk takes a standard action to make a tail attack—its damage is already set by the description, for instance—, but that description does not say that that the tail attack is or at any point becomes, explicitly, a primary natural attack. If a game element applies solely to a creature's primary natural attack, though, then by virtue of the game element applying to a natural attack it applies to the ratfolk's tail attack. See below.)
A ratfolk can take a full-round action to make a full attack, deliver his iterative attacks normally with whatever weapons he's wielding (e.g. shortsword, tailblade, unarmed strike) then make any number of individual and separate natural attacks (like the tail attack of the tailblade) as secondary attacks.
However! During a full attack all "attacks with a tailblade are considered secondary attacks" (emphasis mine). That can't mean that normal iterative attacks, in fact, become secondary attacks: iterative attacks with the tailblade must initially be made as attacks that aren't secondary attacks because iterative attacks normally can't be made with natural attacks, primary or secondary! So, instead, I think that the assumption is that such iterative attack should be penalized as if they were secondary natural attacks: "Secondary attacks are made using the creature’s base attack bonus –5 and add only 1/2 the creature's Strength bonus on damage rolls." Further, based on presentation, this would even seem to affect the tail attack's previously noted damage (i.e. reducing it from full Str mod to ½). (You may want to make the argument that the tailblade's earlier description immutably sets the tail attack's damage. I wouldn't, but you can try with your GM.)
Putting this all together, it's typically unwise for a ratfolk to use the tailblade for his iterative attacks, but if the ratfolk is making a full attack with a shortsword or an unarmed strike anyway then he might as well make the tail attack after making his iterative attacks. The tail attack due to the tailblade becomes essentially just an additional secondary seminatural attack.
(Back to verisimilitude: In my imagination when a ratfolk takes an entire standard action to line up the tail attack, the tail attack doesn't incur the secondary attack penalties because of the caution and precision involved. On the other hand, a ratfolk who takes a full found action to make a full attack during which he wiggles his butt at his foe to make some of those attacks with a tailblade, well, then the secondary attack penalties kick in for those attacks. Likewise, a ratfolk who takes a full attack action to make one or more other attacks then turns around to make attacks with the tailblade or make the tail attack suffers with those tailblade-contingent attacks the secondary attack penalties. My imagination says that it should be difficult for rats to employ a fighting style predicated on shaking their bladed booties. YMMV.)
Note that only a ratfolk wielding a tailblade on his tail can make the tail attack that's facilitated by the tailblade. Get your tail attack some other way, gnolls and kobolds.
"Ratfolk are considered proficient with such [tail] attacks…." To avoid the typical –4 nonproficiency penalty a creature must be proficient with its natural attacks (q.v. the class feature Weapon and Armor Proficiency of the druid). And ratfolk, according to the tailblade description, are proficient with the tail attack that granted by the tailblade. However, ratfolk are not, by default, proficient with the tailblade proper! The tailblade is otherwise a light martial melee weapon requiring proficiency if attacks are to be made with it without penalty. (I suspect many GMs will—and I believe that most GM's should—just give the poor ratfolk a break give ratfolk proficiency with the tailblade, but it's potentially a thing with a strict GM.) And, yes, we're only halfway through that sentence.
"Ratfolk… and can apply feats or effects appropriate to natural attacks to tail attacks made with a tailblade." The presence of a properly wielded tailblade grants the ratfolk a virtual natural attack, the tail attack (i.e. "A ratfolk wielding a tailblade can make a tail attack…"). Such a ratfolk is then eligible for feats like Improved Natural Attack (tail attack) and Feral Combat Training (tail attack). Some game elements that can be applied will be weird or controversial because the tailblade provides the natural attack, but the game's enduring popularity would falter if its players shied away from weirdness and controversy.
To be clear, a ratfolk's tail attack benefits from magic items like an amulet of mighty fists and can benefit from spells like lockjaw and strong jaw and class features like the fighter's weapon training (natural). Also, because the tailblade is, as previously established, a manufactured weapon and due to a ratfolk with a tail attack "adding its Strength modifier to the tailblade’s damage," some game elements that apply to the tailblade will typically also affect the tail attack (e.g. the magic weapon special ability flaming, the magic weapon spell).
In sum, I think the basic idea is for the tailblade to give ratfolk a natural attack without ratfolk having the pay Race Points for it. That such a simple concept yields this much explanatory text means that Pathfinder probably should have developed a clearer and universal way of handling such an effect.
Note: The tailblade is the topic of many Paizo messageboard threads, starting in 2012 when the Advanced Race Guide was published until—at the time of this answer—I think 2019. So far as I'm aware, Paizo never weighed in on the who tailblade issue, but, to be honest, I didn't check all 372 search results.