Just adding my limited convergence knowledge to the thread...
Several (many? most?) Wells-Gardner manuals explain the convergence adjustments fairly well. I just looked at a K7000 manual (p5-7), and a K4600 manual (p4-6). These manuals, and many others, are found here:
http://arcarc.xmission.com/PDF_Monitors/ (scroll down to "Wells..."). I found the diagrams very helpful. I skipped the "color purity" and "vertical centering" steps, and went straight to the "static convergence adjustment". I've got one monitor that appears to need the "precise adjustment of dynamic convergence", but I haven't got around to messing with it yet...
One other thing, don't just try reefing of the adjust tabs lest you break them off. Some (newer) monitors have a "locking ring" that squeezes the assembly to lock them in place. Many monitors have a stripe of glue applied after factory adjustment. If the glue is old and hard, be very careful. I have broken the plastic rings trying to get it off. The best advice I've seen for dealing with this is to use a razor to cut straight down between the rings (parallel to the rings) to allow them to spin, but leaving the glue attached their edges.
I agree with the posters that say don't be afraid of them... they are there for being adjusted. But words of warning are apt; if not carefull and patient, one could easily get frustrated and end up with things worse off. And as cadillacman said, it seems more likely to me that the yoke has become wonked over the years than the ring adjustment being tweaked. That said... I suppose changing components on the chassis could necessitate a convergence adjustment.
Oh, and yes it pretty much
must be done with the power on; preferably with a test pattern (i.e. grid) being fed in.