Before I screw around and let the smoke out of this thing, Does anybody know how to test a low fuel relay?

Andrewh and I went off the deep end tonight and spent a few hours ripping the cluster out of my 72 Imperial. The gas gauge wasn't working and all the typical tests failed.

Bench testing shows that the gauge works great.

Chrysler cut the circuit board to prevent power leading to the fuel gauge. A look at a wiring diagram shows power coming from a low fuel relay.
This car has a Check Gauges light that comes on with low oil pressure, high temperature, and low fuel level.

The relay draws power directly from the fuse block. It sees 12 volts. It has another lead going to ground. The last two leads hit the fuel gauge and the check gauges light.

A 3 volt bench test had the fuel gauge running a little more than half it's range. That tells me it's a 5 volt gauge like the rest of them.
Shooting 12 volts off the fuse block would probably let the smoke out of the gauge.
I can only assume the relay reduces power to 5 volts for the gauge.

If that's the case, how does it turn on the check gauges light?

If this relay is dead, where would I find another one?