Your best bet is to first read the state constitution in regards to tax sales.
Before making repairs to a property before the redemption period is up, check to see if you can be refunded for the repairs by the tax debtor. Each state is different in these regards and a wise investor should read as much as they can on the internet and consult a lawyer before doing so.
An understanding of the world from the view of the tax debtor helps tremendously as well. The debtor often has no clue that you can take their property. The reaction of a debtor to finding someone on their land will be precisely the same you or I would have.
Pay close attention to notification of tax debtor and keep those records as they can help with future title issues such as quieting a title.
From my own experience not in Texas but Louisiana, I only buy vacant land in Louisiana because it requires no maintenance of habitable dwellings. Land in Louisiana bought at tax sale also carries full mineral right ownership (assuming no drilling in past ten years by former owner). Another benefit is that my yearly property taxes are very low and I am able to flip these properties for a much higher rate of return.
@John Fitch have you Googled the county website to see if there is more information. County sites often have tax sale information. It can be hard to find. It won't be on the first page.
@John Fitch ..... In Texas the normal redemption rule is 180 days for non-homesteaded properties, and 2 years for homesteaded properties and agriculture properties. That typically will mean you don't want to do improvements during that time frame in case the owner redeems. According to the property code, Section 34.21 you are only allowed reimbursement for expenses "for maintaining, preserving, and safekeeping the property" which would include insurance, legally-required repairs, payment of municipal liens imposed for health or safety reasons, HOA dues, and utility impact or standby fees.
So you may want to just clean up and rent by the month "as-is" until the redemption period is finished.
You can sell before the redemption period is finished, but likely not with title insurance. So that probably means only to a cash buyer who understands redemption issues / risks. In reality it probably means in any case you will get to hold the property for 2 years before you want to make improvements and can sell it. Even with the 180 day rule, you may not be able to get title insurance for two years.
If you can find the old owner, you might be able to buy their redemption rights, but I think this is probably a rare situation. #1 you might not be able to find them. #2 they might not want sell their redemption rights.
Very few people probably redeem, but with that being said, I am in the process of having a property redeemed right now. Not sure it will actually happen, but the former owner has told me he wants to redeem. So it can happen.
There could be a potential exception to all this and that is with struck off properties. If the sale doesn't happen at the first auction, some counties may "strike off" the property to one of the taxing entities. Some of these wait for the 2 years, before they offer it up for sale again. Then they would likely have no redemption period at that point. These might be referred to resales. Every county seems to handle these differently.
Some auctions warn you about the redemption period, some don't, but you better understand this fully before purchasing and rehabbing and reselling. I'd start by reading the property code with regards to tax sales.
For the most part, @Bruce Lynn is right regarding the redemption periods. It is set in the state statutes.
Necessary repairs can be reimbursed, so if there's a hole in the roof, for example, and you repair it, you will very likely get reimbursed if it goes to court. However, if you replace a roof because you didn't like the color of the old one, that is less likely to get reimbursed.
If you rent out a property, it must comply with the property code and be habitable. There is no "as-is" way to get around that requirement. So a hole in the roof must be repaired before leasing out. But any reasonable repairs that are necessary to be habitable will probably, also, be reimbursable.
Like Bruce said, a redemption is rare.