As often as not my broodies give up with a day or so to go

The red lamps are what you use with a lamb too, yes.
Ceramic bulbs produce heat but not light. Some folk think the ducklings and chicks sleep better if no light. Personally I find that the extra light at night to begin with means they feed more, so grow strongly.
I always put an ordinary desk light on them during the day too, so they dont grow up with funny eyes, thinking the world is red

and then switch it off at night, just leaving the red heat lamp.
Since my ducklings are now in the hall, where I never close the shutters, and their red light is on all night, I shall be getting a reputation.......