I'm going to hate myself for stepping into this discussion.....
I am the radio tech for the Game Wardens on the west side of the state. Game Wardens use either DPS and/or the county channel in their AOR (area of responsibility). Our TPWD towers are only used for internal coordination and you will rarely hear them active. Some state parks have repeaters (San Angelo State Park as an example) because they cover many miles and portable line of site radios will not work. The smaller parks use portable radios and/or 25w mobile radios and use simplex line of sight channels. You may have a hard time picking them up if you are not in line of site of their radios.
As for Game Wardens, they do not wait around all day for a call from dispatch. They are more of an investigative agency and are independent from all other law enforcement agencies. But if they see you break a traffic law (or any other law), they will pull you over to investigate. They are state police just as DPS are, but have wildlife and environmental protection duties that other law enforcement agencies do not have.
Park Police Officers, just like the game wardens use the DPS or county channels. They are responsible for public safety and regulations in the state parks. But just like Game Wardens, they have full fledged law enforcement responsibilities.
As for radio IDs, the Game Wardens use four digit IDs. The first digit is the region, second is the district, third and forth are 04-30. XX04 is always the Captain. My ID is 1230, as I am in region 1, district 2.
There are only 2 radio techs tied to LE, myself in San Angelo, and the other is in Corpus Christi. We have a radio shop in Austin that works for all TPWD departments and is the lead for all communications for TPWD.
Hope this helps.
Jerry N5RV