How do I find that masked man? Really. How do I find a good mechanic?
Here's advice I always give to folks a/b finding a good mechanic. Go to your local parts store (NAPA, O'Reilly's, Auto Zone, whatever seems to be the main store in your town) and ask those guys who is reputable in town. See...the parts guys have relationships w/all the shops and they know who runs a business like a business and who has a jicky jacky shop set up. Reputation travels.
Also....anytime some aftermarket place starts cutting into original wiring on today's cars (post 1996 was when everything really started getting controlled by computers), it can mean trouble. I agree it sounds like they left a wire exposed and it's now touching a metal part of your car (which is a short to ground). If this started right after they installed the hitch/lighting, I have zero doubt this is the culprit. All you have to do is go back and inspect the place they cut the wires and after they removed everything....look at the place they re-connected the wires. For all you know they just twisted the wires and taped it w/electrical tape so it's losing a good connection. The technical "proper" way to repair automotive wiring is to solder, but nobody does that b/c most people lack the skills and there's quicker ways to connect wires that aren't quite as permanent but it seems to be the industry standard these days.
As for the relay..if it is a little plastic box type relay then having a wire shorting to ground makes sense too b/c you have to understand how relays work (the kind that plugs in...not the one integrated into the BCM/computer). A relay is simply an electro-magnetic mechanical switch. If you pop the plastic box off of one, you'll see a coil of copper wire and a thin metal "blade". When electricity is fed to that coil, it creates an electromagnet. The magnetism "pulls" the blade and causes it to make contact to a point that allows electricity to flow to your turn signal bulb. Electricity flowing heats up that blade (which is made of two types of metal). One type of metal is more heat sensitive and it bends w/heat which causes the blade to lift off that contact hence stopping the flow of electricity to your blinker light. This process happens very quickly...so each time your blinker blinks, the magnet pulling the blade, heating of the blade, pulling away of the blade process happens. In fact, there's not one system in the modern day automobile that does not use electromagnetism in some way. It's all very very cool!!
Let us know what you find out. I'm curious. We should start a "Car Talk" thread!