Circuit to give an RF remote audible indication of a mains bulb failure

[Diver300]

Don't think it's critical. I've even used an old shaded-pole mains motor as a current transformer.
View attachment 121904
The blue wire is mains neutral, which goes the scenic toute around the motor core a few turns.
(The fan-heater was just a test load).

I've done something similar with an old transformer. I cut away the old secondary to give space. The old primary of lots of turns became the secondary, and the primary was a single turn. I connected the secondary to a bridge rectifier and an LED. I used it to know when an immersion heater was taking current.