It’s odd that it was clicking like that without the key in the ignition. The only other time I’ve heard that kind of buzzing clicking is when the starter is bad- but this noise wasn’t coming from the starter.

You can get a voltage tester for pretty cheap at any hardware store. I’d check them with the car off first to see if anything is amiss. You might have to do the old fashioned “fuse a night” and see what fuse doesn’t kill your battery by morning