Procedure.. Note this advanced procedure tests a couple of things.
1: Unplug trailer from tow vehicle
2: Connect digital volt meter to trailer batteries and read and record voltage (Write it down)
3: Plug in, Read and record voltage
4: Start tow vehicle, wait at least 2 minutes, read and record voltage
Test complete
Interperting results
If voltage goes up in step 3 then battery is charged by tow vehicle and there is no isolator (Test 1 and 2)
If voltage remains the same in step 3.. No result
If the voltage goes up in step 4 then the tow vehicle is properly charging the trailer batteries.
Additional test you can run....
Shut off tow vehicle.
Disconnect NEGATIVE lead on trailer battery.
Wait two minutes (minimum)
Turn on a light IF it works keep it on for 2 minutes.
If it still works your isolator is not isolating.
Re-connect battery and get isolator tested and replaced if needed.
Note.. All tests are done without shore power connected (and if you have one generator off)