Hi, thanks for the suggestion.
However, its a battery-powered mechanical chime, powered by 4 x 1.5v “C” cells, so 6v DC (not AC). I put a continuity tester across the ring doorbell terminals and pressed the doorbell button, and there was no tone from the continuity tester, so I don’t think it will work.
To be fair, there is a sticker on the back of the doorbell that warns against connecting to a DC supply, so I decided it wasn’t going to work and ditched the old mechanical chime. It seems very strange to me that this doesn’t work, but I have 2 "Ring Chime"s and they’re surprisingly loud (especially for their size) so I don’t really need the mechanical one after all.
Thanks for your help 