MANY states have dispensed with "state inspection stickers" as the cost of maintaining them is much greater than the anticipated revenue - and the hassle to get them - and the service stations that offer them also complain that the cost to do the inspection is much greater than the state allows. Generally, they are a nuisance. Newer Autos/trucks are much more dependable and trustworthy than older models. Texas continues to hold out while many of the adjoining states do not require it.
Regardless, if you have a tail light out or other noticeable problem, you will likely be stopped and given a warning to get it fixed.
From a military point of view, I never had my Texas inspection sticker questioned at any base stateside or overseas - (unless while stationed in Texas of course).
To follow, your Texas driver's license should be annotated you are in the military (also may not have a photo in this case) AND your Texas plates still require the little date sticker showing the plates are current. Both/either can be done over the web or by mail.
AAAAAAAAAAg - Air Force Aggie Architect & Hospital Administrator from Amarillo, Altus, Austin, Arabia, Africa, Seoul, Amman, Arkansas (ret) '65, '69, '73. Track Letterman
"The most potent weapon against basic human decency, in the armamentarium of pure evil, is the self-imposed ignorance and moral decay of the people themselves."