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BBQ Boy - I had a nearly identical issue recently and used the method Jgortva describes. Remove the stern light and touch the wires from the stern light directly to the battery. If it works, then it's not the stern light.

One of the most common issues I find is that the connection points where the bulbs of the stern and bow light connect get slightly corroded. Recently I ran an entire new wire from the circuit breaker to the battery only to discover that the bow light connection points only needed to be rubbed down with a little vinegar.

I recommend cleaning those bulb connection points first as it's a very simple task and the least time consuming of the troubleshooting options.