Not From Texas, but for what it's worth....
I received my commission from the State where I live. So, I am authorized to enforce State laws anywhere in the State, no matter county lines. With this being said, I am most likely not going to get involved in minor offenses that do not happen within my jurisdiction.
Pertaining to your account of the events, bear in mind that while you were on the phone with 911 they may have been coordinating with other dispatch centers because of the jurisdictions you may have been crossing while following the vehicle. Also, that information has to be dispatched to patrol vehicle. I can think of several reasons why the LEO you observed did not take action, the officer you saw:
1. Wasn't dispatched to the call yet so had no idea he was looking for that vehicle.
2. Had a suspect in the rear of his patrol vehicle or some other person he was assisting. (currently on a call)
3. His vehicle was not operational at the time (mechanical failure).
5. He forgot his hat.
BTW...#5 is a joke:D
It doesn't seem likely that a LEO that is unable to pursue a violator into another jurisdiction would hang out at the county line.
Integrity is doing the right thing even when people aren't looking.