Jane:
I second what Jay was saying, and if your mast head is like the 32 then there are 6 sheaves in the mast head 3 fwd and 3 aft with 2 aluminum plates, one on each side of the center sheaves, keeping the port line running on the port side ctr in the ctr and yes the starboard to the other side.
Some additional thoughts: how long ago did you service these (remove check, clean and regrease) ? I have done this twice in 17 years = not the best, and should have been every 5 but I am lazy (I inspect once or twice a year while in the water). I do hate to do this work, But both times I have had the mast off the boat. If YOU (not some one else) has inspected and regreased these in the last 4 years ? Maybe just pushing the pin back could work?? but if not (which sounds like the case) I would take the mast down and do all the service on the ground. But if you are on an island 500+ miles from a yard I would bring a rag up and feed it through under the (sheaves, and tie it off so that things can not fall down into in the mast. And also rig a bucket to bring tools / parts up and down.)
Climbing the mast is indeed not that much fun when you know everything should be right, Not sure I would do that, knowing something may be wrong, but with that note, as long as you have a safety you may not fall? as the line is captured in the mast head, but you may need the fire dept if it fails as the line would have to run over edges inside the mast head which would not work well if you try to come down.
SO I would never do what you are asking, unless there was not the option to take the mast down i.e. there was not a yard for 100's of miles which I could motor to (fixed mast) mine will tabernacle and I would take it down to do the above. Working at the top of the mast is not fun for me at all. While on the ground (sawhorse) I had the above parts fall to the ground 3 times when I tried to reassemble them, which required cleaning regreasing and trying again, so if you drop stuff down the mast UGH!!!!!!!!!!!!!! this will not work!
My sheaves were aluminum with bronze bushing running on a ss tube (pin) last service I flipped them as there was some (Not allot but some) ware on the ss tube (pin). If the cover came off, I would guess you have issue with the sheave griping the shaft which would turn the shaft which would try to jack the little plate off the mast; but that is only if your setup is like that on the w32
Hope this helps
Norm
p.s. I reread your post, and if true, last service 1974. you may want to order new sheaves, plates [not cover plates but the ones between the sheaves] and pins from Bud before going up as it is likely the bronze bushings are failing or they have eaten into the ss tube (pin) and made it not round.