Taking Cover with Tower Shields provides omnidirectional benefits of standard cover, but does not otherwise count as cover for the wielder in any direction
After doing some book trawling, I believe this is the correct answer to this question. This is because of a few reasons. On the sidebar on page 462 it details something called Subordinate Actions with the relevant text as follows:
An action might allow you to use a simpler action—usually one of the Basic Actions on page 469—in a different circumstance or with different effects. This subordinate action still has its normal traits and effects, but is modified in any ways listed in the larger action. For example, an activity that tells you to Stride up to half your Speed alters the normal distance you can move in a Stride. The Stride would still have the move trait, would still trigger reactions that occur based on movement, and so on. ...
In this case you have the Tower Shield which allows you to use the Take Cover Action even if you ordinarily wouldn't be able to to increase the circumstance bonus to AC to +4, lasting until the shield is not longer raised. Other than the ability to use it without meeting the requirements of Take Cover, nothing in this line of text contradicts the text in the Take Cover action, which, after detailing the ways it upgrades Standard Cover to Greater Cover, has the following:
If you would have standard cover, you instead gain greater cover ... Otherwise, you gain the benefits of standard cover
This gives a +2 circumstance bonus to AC, Reflex vs AoE, and some Stealth checks. Note the wording though, you gain the benefits of standard cover, but you do not actually get cover (note the difference in wording between "gain greater cover" and "gain the benefits of standard cover").
This is important as in discussion about this matter it was pointed out that the application of a stealth bonus is a bit absurd for a giant tower shield, namely that it would be silly to be able to hide behind a giant slab of metal you yourself are holding. As this does seem wrong I did some more digging, and in fact a further look at the Hide action shows that in order to hide you must actually have cover:
You huddle behind cover or greater cover or deeper into concealment to become hidden, rather than observed. The GM rolls your Stealth check in secret and compares the result to the Perception DC of each creature you’re observed by but that you have cover or greater cover against or are concealed from.
This might sound like a weird distinction to make or splitting hairs, but even without Tower Shields in the mix, this differentiation prevents absurdities. Lets take a look at the requirements for using the Take Cover action normally:
Requirements: You are benefiting from cover, are near a feature that allows you to take cover, or are prone.
This means if you drop prone anywhere you can use the Take Cover action to gain the benefits of Standard Cover (just like with a Tower Shield). If getting the benefits was enough to qualify as actually having cover for purposes of hiding then you'd be able to lay down in front of a giant crowd, Take Cover, and hide from all of them. Incidentally this also means that while you can raise the cover you get from other medium allies from lesser to standard using Take Cover, you also can't Hide behind them (unless of course they have a Tower Shield raised or are two sizes larger).
So in very long winded answer to your question, regardless of the direction you gain a +4 Circumstance bonus to AC, a +2 Circumstance Bonus to Reflex vs AoE, and a +2 Circumstance Bonus to Stealth Checks to Hide, Sneak, or otherwise avoid detection. However, you do not actually have cover and cannot take actions that require it unless you're getting it from another source or are otherwise able to avoid the requirements.