That is only if you are not a US citizen. HOWEVER, if this was a dealer, your paper driver's license would not work for Texas ID anyway, if it doesn't have a photograph:
27 CFR 478.11:
Identification document. A document containing the name, residence address, date of birth, and photograph
of the holder and which was made or issued by or under the authority of the United States Government, a State, political subdivision of a State, a foreign government, political subdivision of a foreign government, an international governmental or an international quasi- governmental organization which, when completed with information concerning a particular individual, is of a type intended or commonly accepted for the purpose of identification of individuals.
All that is required according to the same CFR for residency is presence in a state with an intent to make a home in that state (no minimum time requirement is specified):
State of residence. The State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State. If an individual is on active duty as a member of the Armed Forces, the individual's State of residence is the State in which his or her permanent duty station is located. An alien who is legally in the United States shall be considered to be a resident of a State only if the alien is residing in the State and has resided in the State for a period of at least 90 days prior to the date of sale or delivery of a firearm. The following are examples that illustrate this definition:
Example 1. A maintains a home in State X. A travels to State Y on a hunting, fishing, business, or other type of trip. A does not become a resident of State Y by reason of such trip.
Example 2. A is a U.S. citizen and maintains a home in State X and a home in State Y. A resides in State X except for weekends or the summer months of the year and in State Y for the weekends or the summer months of the year. During the time that A actually resides in State X, A is a resident of State X, and during the time that A actually resides in State Y, A is a resident of State Y.