I'm actually litigating two adverse possession cases right now, with highly contested facts, so all of this is pretty fresh in my mind. Here are my two cents:
First, it doesn't sound like a tax sale is really relevant -- you have said the taxing entity doesn't even recognize the parcel, and you said no one can find out what happened to the property since 1926. When I see this, the property has "theoretically" devolved to the heirs of the owner in 1926.... and they typically have no idea, and aren't interested in the property anyway -- of course, this all changes if there is oil/gas production. They come out of the woodwork quite interested.
So what should you do?
FIrst, I'd say you ought to speak with an attorney. There are a lot of great suggestions here, but we dont' know enough facts from what you've said to really render solid advice. Further, I do have to tell you that what I'm about to say can not and should not be considered legal advice... I'm merely giving you an outline of a few possible paths an "adverse possessor" could take. Adverse possession is extremely complex, fact intensive, so you really need to chat with an attorney so that the best path (which may or may not be one of the following) can be devised based on your specific facts.
I typically tell people with title issues with a strong adverse possession element that they usually have a few common options. The first route is what many above are suggesting - with affidavits, fencing, publications, etc. A second move would be to combine these moves with a quiet title suit... Winning this type of suit essentially gives you rock-solid title (yes, there are some exceptions, such as failure to include claimant(s) in the suit). A third option may be to cure the title... though this has risks as well.
However, if you don't bring a quiet title suit, then technically you won't have marketable title. However, many people are content relying on "limitations title," meaning that they are fine filing affidavits of use and possession, fencing, doing other actions to bolster an adverse possession claim, etc., and relying on their ability to defend against future claims, such as trespass to try title claims by a different possessor/record title owner.
No Suit Route: So if you wanted to go this "non-suit route," then the filing of an affidavit would assist you a great deal, the fencing could also be a crucial component depending on the acreage you currently own on record title as well as the acreage of this other tract. Petitioning the tax assessor to begin assessing you taxes, and paying those taxes could also really bolster your claim. I'd chat with an attorney to come up with a list of actions you could take to best bolster your claim -- again, adverse possession is extremely fact intensive, so no general "hey, just do 'x,' 'y,' and 'z'" will work. However, this route has its limitations, and you need to be aware of them: first, future buyers are usually not interested in purchasing land from someone who only owns "limitations title" and I've never seen a bank that is keen on the idea. So if you have these burdens on selling the property, that can be enough to push a lot of owners to do something more... one option of which may be described below.
As another quick note on this route, affidavits of use and possession can be very simple, and you could DIY it. But I've seen a good deal of these affidavits that are worth very little. I could literally write an entire series of articles on the problems I've seen in 'title clearing' affidavits. Texas has some very thorough case law on adverse possession, and a lot of unique factors can bolster a case - many of which may not be that apparent which facts can make or break your case. Who built the fence, how was the fence maintained, was the land used for grazing, what type of gates were installed, etc. Also, the person you have swear to the affidavit can have a great deal of impact. I guess my point is that you should approach the affidavit with a keen eye... it's not something to "pencil whip."
Quiet Title Route: Another route, as I mentioned above, would be to file a quiet title suit. From what you've said, this suit would essentially be filed against 'unknown defendants,' and as another person said, publication would come into play here. I would also suggest publication in a normal newspaper, rather than some sort of legal newspaper - the idea is to make it look like you've made a diligent effort to reach any potential claimants to the land. This can have two purposes - one of which is adverse possession specific, the other of which is a specific required civil procedure device, required by law as a prerequisite to filing this type of suite. Texas has a great deal of law regarding this type of publication, so it certainly isn't anything too terribly unique.
From the sounds of it, i may very well be that no one would even respond to this suit, and you could possibly have a very quick and easy claim. As far as legal services go, if nothing any more complex than this comes up, you'd have a pretty darned small pricetag. After this suit, if you were successful, you would then be the rightful legal owner of marketable record title. You could much more easily sell it, banks should be satisfied, and you'd be set.
Curative Route: Finally, you could "sure" the title without any law suit. Many ways you could do this, but one would be to obtain "quitclaim deeds" from the 1926 owner's successors (usually this is the heirs). This could involve costly heirship research, and has several other downsides. For example, I have seen people shy away from this move due to the fact that they fear "tipping off" these successors as to their claim to the property. Additionally, I have seen these takers immediately specify a pricetag for the quitclaim deed.. sometimes it's legitimate, other times these heirs are just trying to get $$. Just to name another risk of doing curative, sometimes these offers can really hurt your adverse possession claim. I've seen these offers fall through, and later destroy an adverse possession claim because the heir comes back and says "well how can you say you have been treating this land as though you are the rightful owner if you are out there sending me offers? it sounds like you were treating ME as the rightful owner." For the legal types, the idea is that this offer may hurt your ability to prove that your possession was "exclusive" and "hostile."
Conclusion
Not to repeat myself too much here, but I'll tell you that my best help is that you really ought to get with an attorney and discuss the options. No one on an internet forum can read one quick paragraph about your scenario and give you solid adverse possession advice. It's simply too complex, and there are too many routes available. I mean, heck, not even my long post above goes through all the options...