Odd indeed
Jamie -
That truly is an odd sound. 35+ years of using belt drives and I've not heard a click quite that loud.
We had an issue when I was a kid with our first machine with cabinet "creaking" which my dad thought was electrical sparks, and sure enough, there can be sounds from the service panel area that can make creaks that sound like loud clicks or sparks, usually only in spin.
Your click sounds very "un-muffled" like there's nothing in the way of the noise source and the ear. Internal transmission noises have to go through oil and the trans. cover before getting out in the air, so this has me puzzled a bit. The pulley idea above may be a very sound one, and easy to verify and fix.
If this is a transmission problem, clicks often come the agitator gear fork, especially when it's not under heavy load. The part will click at the end of each stroke (unless load is put on the agitator, even by holding the top by hand). The noise worsens as the fork wears, and is louder if the transmission has lost a lot of oil. The gear fork is what pulls the machine in and out of agitation inside the transmission.
Next time you use your washer put it on fastest agitation and grab hold of the agitator, and see if you can muffle or stop the clicks - if so, the noise may be inside the transmission. If you have a belt/pulley problem, the noise will probably get louder under load.
Please keep us posted, I'm curious.