I had a very similar problem, two of them actually. On one occasion I could hear my strobes through the headset, but not all the time. Long story short there was a nut on my main solenoid which was a eighth of a turn loose, and every now and again it would arc. For reasons I don't understand it made the wheelen strobes broadcast through the headset. It also played havoc with the charging system, as current couldn't get back to the battery regularly enough to keep it charged.
On a second occasion my voltage regulator malfunctioned, keeping the battery from charging. With all the current coming off the battery I would notice the radio lights pulsing in sync with the strobes.
The voltage regulator looked new and it would work some of the time, which kept me from being able to diagnose it easily. I found that by grounding it with the engine at 20K rpm my volts skyrocketed, thus confirming it was the problem.
Something that might help you figure out what is going on is a better voltage meter. I took a radio-shack digital voltage tester and wired it into a 12 volt plug, then plugged it into my cigarette lighter. It gave me a much more precise picture of what the electrical system was doing and I could instantly see when the voltage would drop and climb.