My fuel gauge was working intermittently and recently stopped functioning. I put a test light on the wire to the sending unit, no light, but I'm not sure if that circuit carries enough power to make that a valid test. I'm not experienced in diagnosing electrical stuff. Any thoughts on where to start?

Do the rest of your gauges work? Check for loose connections.... I would start from the cluster and trace to the tank

Phil will be along to give you the right way before long

You are on the right track. You can use a test light at the tank and then behind the dash. There will be enough juice to turn on the light but it is interminent so it blinks. If you got power to the tank then it's the unit in the tank. If there is no power at the dash then it is something behind the dash or gauge itself. Just my .02.

The other gauges work just fine and the wiring harness is a Centech I put in about 3 years ago, so I'm thinking it's the gauge or the sending unit. I don't have a multimeter. Is there a way to test the sending unit without one?

You can use a test light. Just ground the test light and probe the wire to the sending unit.