A relay wont stop the problem. A relay you would buy for something like that at Auto Zone etc... takes approx 1/10th of an amp, to trip. Youre already getting power from a bleed through somewhere, and that little amount of current would trip the relay and allow the issue to continue.
Case in point, when I installed my light bar on my bull bar, I wanted it to have its own switch in the cab. BUT, since I didnt want to have to reach for my dimmer switch to kick off my high beams, AND reach for a switch for the light bar at the same time (if I met an oncoming car out in the stix) I fed the switch for the light bar, off of my high beams.
So.... heavy wire from battery through inline fuse to relay, and out to light bar. Light wire from high beams, through switch in the cab, to relay. This way, I can run my high beams without running the light bar. When the light bar switch is on, turning on my high beams turns the light bar on.... dimming them turns it off.
BUT...... If I leave that switch for the light bar on..... when I open the door (truck off, key off, lights off) the light bar flashes. Why? Because a small pulse of current is sent through the lighting system, including the high beams.... when you open the door and the dome lights etc... come on. This pulse of current isnt enough to turn on any other lights or make them flash, but it WILL make my light bar flash quickly like a bolt of lightning lol.
So, I know first hand that if you have any small bleed through of current, it will still trip the relay, and you would still have the problem.
I just got my LED lights cut into my new bumper. When I hang the new bumper, I am wiring the lights off a switch panel I made, in the cab. I dont need those bright back up lights often, and dont want them coming on every time I am reverse..... blinding everyone in parking lots etc... at night
The resistors that sourdoughben listed would be a better thing to try, not a relay.