Graeme wrote:

Intrigued by Andy's suggestion of drilling an LED bulb.

Not a "bulb" just an LED.

straw-hats have an internal conical reflector so they tend to shine
sideways, which I assume your rotary flasher needs? You'd need to drill
your own dimple for your pivit e.g with a countersink drill bit, or
chamfer router bit, you wouldn't want to drill too far at risk of
damaging the LED die, so buy a big bag cheap from china to allow
experiments, e.g.

https://www.aliexpress.com/item/100pcs-lot-Ultra-Bright-0-75W-F8-White-LED-8-mm-Straw-Hat-Light-Emitting-Diodes/32286410626.html