interesting, I never thought that could cause clicking, I always thought that that would make the drives just refuse to work outright.
If there's no signal from the head assembly at all, the drive will still spin up and attempt to seek, but when it finds that the heads "aren't moving" or that they are not in the position they are expected to be in, the drive will snap them back to the home position very quickly.
Hence "clicking" or "ticking" or "click of death," whatever you want to call it.
Cleaning the contacts is a great solution, even some older drives can benefit from this. It's by no means permanent and after a drive starts having problems I typically back it up daily until I can get a replacement, at which point I wipe the original drive and toss it out or pull the PCB (sometimes the PCB can be bad).
Sometimes, replacing the PCB can assist in making some of them work again. Sometimes things like amplifiers or actuator electronics will fail and cause it to click. If you've got another drive of exactly the same kind, you can always try putting the other board on.
Loose or dirty contacts and broken solder joints are the most common issues I find with hard disks of any age, and I mean any age. Micropolis 20MB hard disks all the way up to relatively modern WD 500GB SATA disks so far.
I've never really been able to get the freezer method to work reliably. Some drives will "work" after (run for about 2-3 minutes and die again), some will """work""" (spin up but not be recognized or appear as unformatted / empty to an OS), or just have no effect at all.