As Don suggested, it may be the sending unit. There are a few wires going into the tank. The Black and Yellow/White go to the sending unit. Disconnect the connector at the tank. Measure the resistance between the Black and the Yellow/White using your meter.
About 40 ohms is a Full Tank.
About 120 ohms is a 1/2 Tank
About 260 Ohms is an empty Tank.
See what you read. All you said is the gauge went "Out". You did not say if your gauge is pegged on Empty or Full. But I think you get the idea of what you should read with your meter.
GimmeFuel; the wires Hoople explains in his reply are located under your fuel gauge...just need to get it unmounted & test wiring w/meter. If one of the wires are broken/damaged - should see right away.
I can only give you the needed tricks or "know how" on how to diagnose your problem.
It doesn't take the place of having a Harley Service manual which lists the steps on how to replace the sending unit if it happens to be bad (reads Infinity with meter).
I'm not familiar with F.B. fuel gauge location, but my Dyna fuel gauge (where the left cap would be) wires come out of the bottom of the tank. Check the connection there.