This resource from the Attorney General of Texas’ website offers a breakdown of the laws pertaining to the purchase of used (pre-owned) cars in the State:
https://www.texasattorneygeneral.gov/consumer-protection/automotive-scams/buying-new-or-used-car
Just one of the sections of that page reads:
After the Sale
Under Texas Law, you do not have 3 days to cancel the purchase like you may with some transactions the dealer is required to register and title the vehicle in your name within 30 days, regardless of if you owe money on the vehicle to the dealer or another financier. As soon as the vehicle is registered in your name, the dealer should provide you with the original title application receipt from the Tax Assessor-Collector’s office.
If you owe money on the vehicle, the original title will be sent to your financier. If you pay in full for the car when you purchase it, you will be mailed the original title.
Keep all payment receipts and other documents in a safe place. Do not keep them in the glove compartment. If the car is stolen, or if a dishonest dealer illegally repossesses the car, you will have no records of ownership or payment.
Make your payments on time. If the dealer or your Lender says that you can change the payment dates, or pay late, get it in writing. Get a receipt for each payment.
Texas dealerships have the legal right to repossess your car without prior notice, even in the middle of the night. Keep your records safe and up to date for your protection.
It also links to the Texas Lemon Law which can be found here: https://www.txdmv.gov/motorists/consumer-protection/lemon-law
Thank you for the suggestion of this resource goes to HiLine Motors (map here).