The Tax Department
The local Appraisal Dirstict values real estate in each County for the purpose of collecting property taxes. They are very good at keeping track of property ownership.
Their database is available to the public. Most have public access phone numbers. This requires a phone call. The database can be searched by name or address. In addition to property information they track deed information going back several owners. This can be helpful. Their records for prior years are archived at the Texas State Library.