RF was born in El Paso County, so unclear on when he began residing in Alpine. (El Paso is one of the closest big cities to Alpine, so could have been then; he definitely went to Alpine schools). His father died in 2003 and most of his extended family on his father's side lives in Austin. RF's FB page seems to indicate that he wanted to move to Austin in 2015. All of the above is public information available online for free.
Stripes is the one of the few places open late. There's no need to go there for gas; there are plenty of unattended gas pumps but if you need to pay cash, you'd go there. You'd also go to get something to drink; it's one of a few places with fountain drinks. If you were trying to avoid being seen, you wouldn't go there; it's very well-lit, unlike most of Alpine, which is extremely dark at night.
There are a couple of trains per night that come through with horns and I'd be curious to know what times they came through that night. If you needed a noise cover, that would be it. Most people are well-acquainted with the sound of a gun firing and a TV blaring would not change that.
There is a pipeline being built that runs within a mile of the hospital. There's massive construction debris over more than 100 miles in addition to segments of pipeline large enough to hide a person in. That entire area cannot be searched without permission from the pipeline company because doing so is trespassing and will get you arrested. There needs to be massive pressure on the owner to allow a search.
The rainfall this year has been unusually high and the grass and brush is far taller than usual. The Davis Mountains are indeed more remote and with far less cell phone signal or Internet. They'd be an ideal place to hide, but you risk being pulled over by LE on the 30 mile drive there.
US Border Patrol has a very significant presence in Alpine; less so in the Davis Mountains, but it's there. They have a lot of canine resources that could be used if locations are narrowed down. They routinely patrol all of Brewster County. They will be coordinating with other LE.
I am a very frequent visitor to the area and a parent of two similarly-aged daughters.