From what I can tell, using Two-Weapon Fighting and having a Light weapon in your offhand at best reduces the penalty to -2/-2. Is there an official 3.5 method of completely eliminating this penalty? I do intend to eventually progress into further TWF with Improved TWF as well, but planning out my feats and the like I'd like to find a way to get rid of that last -2/-2 penalty if I can.
Yes, if you can get yourself a second head (since multiheaded is an inherited template with at least +2LA it's probably quite difficult to get until later on where adjusting your character's race/templates becomes cheap and easy). Also, this is obviously not something you "progress into" at all, you either have it (and make all TWF feats obsolete) or you're stuck with the last -2/-2, so if the chance of your DM allowing the growing of a second head mid-campaign (or you starting with a +2LA template) are slim, you should go with normal TWF feats anyway.
Savage Species page 125:
Superior Two-Weapon Fighting or Superior Multiweapon Fighting (Ex): Because each head controls one arm (or analogous weapon-using limb), a multiheaded creature has no penalty on attack rolls for attacking with multiple weapons, and the number of attacks and the damage bonus for each weapon are calculated as though the weapon were held in a primary hand.
It basically allows you to wield two weapons of your choice (even two non-light weapons) and get each of those weapons' full attacks at no penalty whatsoever.
There is the Tempest prestige class in Complete Adventurer (pp. 81-82).
It reduces the penalty to 0 at Tempest lvl 4 (with light offhand weapon), but restricts you to light armor. This is also somewhat offset by a +3 unnamed bonus to AC (at Tempest level 5).
You also get benefits of some weapon-dependant feats (like Weapon Focus) to both weapons (you get Weapon Focus for a scimitar and also apply it to the dagger you hold offhand).
To become a Tempest you need BAB +6 and several feats, all Spring Attack and TWF related.
Yes. The Tempest prestige class (Complete Adventurer page 81), available to sixth-level fighters, gains the Ambidexterity ability.
Ambidexterity (Ex): For a tempest of 2nd lvl or higher, her attack penalties for fighting with two weapons are lessened by 1 (from -4 to -3, or from -2 to -1 if the off-hand weapon is a light weapon). At 4th lvl, the attack penalties are lessened by another 1 (from -3 to -2, or to +0 if the off-hand weapon is a light weapon). The character loses this ability when fighting in medium or heavy armor.
(Read about in Jonathan Drain's answer to a related question.)
Two levels of the Bloodclaw Master prestige class from the Tome of Battle gives superior two weapon fighting, negating the penalty, but it only works with daggers or tiger claw weapons. You also need 9 ranks of jump to get in, and three tiger claw manoeuvres.
Given how synergistic those manoeuvres are with TWF, I'd recommend doing it anyway, and a single level dip into Warblade, from the same book (and recommended by me to anyone who uses a weapon heavier than a dagger) will give you all three, along with a d12 and full BAB.
Alternatively, if you're more of a rogue build, Swordsage gives a lighter combat chassis, but with a few more manoeuvres known, and the shadow hand manoeuvres in particular complement a rogue nicely.