Unhook the leads from the lamp, check the current with an ammeter. Wiggle the wire at a few places. If the wire is broken, you see the current drop when you wiggle things around.
The typical break point on wiring is right at the neck of the spade connectors, and you can check that just be feeling if it's flexing too much (meaning most of the copper strands are snapped.)

I'm going to guess that what you have is a bottle generator, since you mention moving it from the rear to the front wheel. If that's the case, the intermittent working in the rain is likely due to contact wheel slippage against the wet tire. That's why I mentioned the wire brush roller replacement. I saw them on one of those two sites for using a bottle gennie in wet/snowy conditions. The wire brush grips far better than the normal rubber capped friction wheel.