Some trucks turn off the hot wire to the trailer plug when the ignition is turned off, but yours appears not to be one of them. Your rv batteries are being drained most likely because you have something in the rv that?s pulling more power than your truck alternator can supply. Here?s how to run that down.
1. Buy a cheap 12V test light at an auto parts store.
2. Unplug your trailer from your truck. Make sure everything in your rv is turned off.
3. Disconnect the ground wire from your trailer batteries.
4. Connect the test light to the ground wire and the battery ground post. The light will most likely come on, indicating something in the rv is pulling power.
5 inside the rv, pull the 12v fuses for the CO/propane detector and the radio. That?s because the detector always pulls power, though it?s too little to be causing your problem. Same thing for many radios which have a small power draw to remember presets and time.
6. Check your test light. If it?s off, you probably don?t have a problem.
7. If it?s still on, doing one at a time, pull each fuse and check the test light. Leave the fuse out until you?ve done them all. I?d suggest taking a picture of your fuse panel so you can put them back into the correct slots.
8. When you pull a fuse, if the test light goes out, you?ve found your problem circuit. If it?s something you?d expect to pull little power, you probably have a short you need to run down. If it?s something that can pull more power, see if somehow it got left on.
That?s a start. Welcome to the exciting world of RV electrical problems.