Alan,
I'm a bit confused here as to the order in which things came apart. You say you took off the "timing side covers". By this, do you mean the three- corner timing cover, or do you mean you removed the valve adjustment covers. I was thinking, maybe, interference between vavle cover(s) and adjusters, if the adjusters got loose or were replaced with too-long aftermarket parts. However, with the clicking at low RPM, my next thought was a sticky valve guide that, somehow, let the valve snap back after a short bit of time. Having taken the engine apart to the extent you have, it seems not that big a leap to release the vavle springs and feel the valves in their guides. Maybe all that would be needed is Molyslip Oil Additive or some other top-end lubricant.
Also, check your pushrod ends to be sure they are tight in the tubes and not hopping about. I'm not sure if I can logically connect that to the clicking noise, but as long as you are in the vicinity, may as well check it.
All this said, I would check out what Markus (MG) said as well, and hope for yet more ideas.
Richard L.