My guess would be relay, it's triggered by the accessory wire. When I turn off the ignition the driving lights are turned off, ie. no current to relay, here's the problem, the driving lights will slowly relight. Start it up, the lights are on and can be switched on and off by the manual switch. Shut it down and a few minutes later the lights will light back up again. Decided to just remove the hot from the battery until the problem is solved.
Eli, unplug the trigger wires from the accessory circuit in the boot. If the lights still come on, I think the relay has failed as you've guessed.
If not, check the accessory circuit in the boot for voltage with the key off. There should not be any.
This is a weird one though. Never heard of it before.