There is usually enough traffic that there will be someone along the road at least every five minutes, most of the day. This is an area where the custom is to stop to see if you need help, particularly if you flag for help.
Border patrol will likely be coming by at 30 minute to hourly intervals. If you are stopped for very long, you will be caught by aerial surveillance and someone will definitely be coming to find iut what is going on. All of thiese reponses likely quicker than any road service provider.
Cell coverage is sparse in the American west, doesn't have to be west Texas. I am within 20 minutes of dead zones covering 100-200 sq miles, in NE Oklahoma, southern Kansas, you will find the same across much of the Great Plains, in the mountains, western deserts and high plateau. Wasn't that long ago there was no cell coverage anywhere, we managed our road trips, not just the desolate West. Wife, daughters traveled these empty roads routinely before cell phones, still travel through them where the phones don't work.
If it is a real issue personally, you might consider renting a satellite phone. This is what we do for field work in communications dead zones, not because we are there, but because what we are doing there is physically dangerous, with high risk of injuries needing emergency medical attention and evacuation.
