MUCH too whimpy a system with that wiring in the accessory system.
You should be using 10 (Or better) guage stuff. Simply run from car battery with hefty wire, put an inline fuse in, tie the wire off at handy unhot places under the tug and to a proper connector at the car and pigtail.
Mine does not have an isolator, I just remember to unplug the tug when I get set up.