What would cause the ceiling fan light to blink or shut off?
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.