Rythmic noise at idle - Absent with belt removed - Fixed!

Hi,
I was wondering if I could pick collective brains. As part of the rolling restoration on my Coupe I'm having a bit of trouble working out what is causing a noise when the engine is idling.

When started it makes a rhythmic sort of 'chirp' (not squeal) that goes away when the revs I raised. You don't notice it when driving, just idling. Even my daughter asked what the noise was! (Makes no difference if ac is on or off)
It sound like ancillary belt or something in that area so I removed the belt and ran it again - no noise.
I checked the alternator and that was quiet, I checked the ac pulley and that seemed quiet so I've changed the tensioner and fitted a new belt but the exact same noise is still present.

Using a mechanics stethoscope didn't seem to pin point it either. I'll try and get a recording.
Does anyone have any other ideas please?

Thanks,
Andy.

Water pump?

Good shout, but it has an electric pump as it's a Coupe.
Thanks though.

It’s got to be something the belt goes round.
Have you checked the crank pulley

I did glance at the crank pulley, nothing looked odd. I think it is a harmonic type pulley but there didn't seem to be any play.
As you say it's got to be something the belt goes round as the noise is absent with it removed. Should be obvious....
:headbang:

Yes it’s a harmonic balancer pulley.
No splits in the rubber?

Managed to capture some sound clips today.

1st clip is running with the belt, 2nd without.
In both clips there is a half second horrible noise on start-up which I also don't know what it is. Obviously not belt related as it does it on both.

On first clip the rhythmic noise is most obvious around 1m 30 and beyond.
Bit stumped what either noise is??

https://youtu.be/3KKOwDoP7U0?si=HcpfJQs2aDEa-NS8

https://youtube.com/shorts/IUTJyIqLstI?si=c5BkWa8AFnxmd4tm

Just to follow up on this. It turned out the alternator pulley was faulty. I didn't realise the pulley has a one way clutch mechanism. Mine was seized so didn't slip in one direction.
I tried to replace just the pulley but it didn't come off, even using the correct tools, so bought a new alternator.
On to the next thing....