I'm a bit embarrassed to post this but apparently my rattle was caused by the phone charger I'd plugged into the power socket between the seats. This one had a metal (probably aluminum) case that was contacting the inside of the socket, causing the metallic tapping noise.

 

Don’t feel bad, I’ve done the exact same thing. I also did the same thing with my garage remote on the sun visor.

 

Thanks for the follow-up. I'm sure this will help someone in the future.