Moved from another thread ...
While I'm not familiar with the SE's low fuel light relay and how it is wired into the cct, if you only have one wire connected to the threaded stud on the sending unit, you must be missing the ground wire connection. That one wire on the sending unit still needs an electrical path back to the -ve of the battery. If there is no ground connection, you are open circuited. I remember reading a thread where you said your low fuel light blinked from time to time. Does the gauge work at all?
Thanks for your help guys. I don't want to hi-jack this thread with my problem. That said, my gauge works, but it was off by about 1/8 - 1/4 tank. The light was on constantly. From the service manual, I discovered that the black wire from the regulator should have been replaced with the blue wire from the low fuel relay. Once I fixed that, the low fuel light blinked on and off with about a 10-20% duty cycle about every 30 seconds while sitting still. And while driving over bumps it exhibited what I would describe as an intermittent. I discovered the LFE light and fuel gauge work in the accessory position of the ignition switch. So I'm gonna have my wife watch the light while I try to move some "groundy" things around back by the tank. This might turn something up. Since the low fuel relay contains thermally actuated bi-metalic switches, I think the time it takes to register a change if fairly slow, but maybe the grounding of the relay itself has some affect.
There are a lot of electrical connections that are returned through the chassis, and don't have separate ground wires. The dome lite, oil pressure sending unit, horn, etc. I think the fuel gauge is one of them. But I'll double check this weekend.
I'll copy this over to my thread so I don't drag this off on a tangent from the OP.