An intermittent problem like this could be caused by a combination of a loose connection and the waste heat from the bulb. As the bulb and light fixture heat up, they expand eventually causing the loose connection to be broken, turning off the light. With the light off, they cool down and shrink, remaking the connection so the light turns on again.
This could be dangerous as you could get arcing across the connection at the points where the light turns on or off, which can cause electrical fires.
To find and fix the problem:
- Try a different light bulb; this will tell you if the fault is with the bulb or the fixture.
- Turn off power to the fixture at the service panel. Open up the fixture and check that all the connections inside it and in the ceiling box are secure. Close up the fixture and reapply power.
- If you're still seeing the problem, it's likely a fault in the light fixture itself. I'd consider replacing it at this point (or there are repair kits, depending on your skill and comfort level with diagnosing the fault and doing the repair).
Filament a likely culprit, but is the fan perfectly balanced? We all assume not perfectly. Bad connections, even good ones, break with enough movement over time. Potential chain of events:
Power on - rush of power bridges air gap, or gap doesn't exist, connection holds together
Running - something gets hot or vibrates loose, loses connection
Stop - cooling or lack of vibration allows physical gap to close enough so that...
Power on - rush of power bridges air gap, connection holds together, repeat
The connection could be filament to post, switch to wiring, internal in the fan, the place where a rat ate away connection material, anywhere in the current loop really, but filament, switch, and internal to fan are my top three suspects.
Best Answer
Assuming the light itself isn't bad, then the combination of a dim light and the dishwasher making it go out sounds like a break in a wire or a corroded connection. A break or corrosion can allow enough current to pass to light the bulb dimly, but when a higher current is called for the resistance of the break or corrosion goes up, causing an apparent total failure.
See https://diy.stackexchange.com/a/27285/82