Relay Clicking behind my dash -- what is it?

I've recently developed an intermitent rhythmic relay clicking (tick-tick, tick-tick) that sounds like a softer version of the turn signal relay coming from the left side of the dash in my '87 Ram 50. The odd bit is that if I put any load on the electrical system (turn headlamps on, touch the brakes to light the brake lights, turn on the vent fan...) it immediately goes away, but comes right back when the load is removed.

It's almost like I had an old-style mechanical voltage regulator back there that was starting to get noisy. :P

What the heck is back behind the left side of the dash that might be doing this?

I'm guessing that whatever the relay feeding is partially grounding. When you allow an easier path to ground but turning on one of the accessories, the current drops off enough that it stops acting up. There are some relays on the left side of the drivers foot well. Try removing them 1 at a time. When my temp sensor for overdrive was dying on me, the relay would occasionally start clicking on and off like you describe