Hi Tandyman (BTW, we use our real names here. You should put it in the signature section of your user setting and it'll show up on all your posts, past and present),
That sounds like the old screeching tape counter problem that's very common to the RS series machines.
If you open the back of your machine (power off!), you can see that there are two white pulleys and two belts that connect the shaft of the reversing roller and the tape counter. First try putting a tiny bit of oil (as small a drop as possible) on the shaft of each to the two pulleys.
It could also be the counter belts. They tend to get hard with age and kind of oblong shaped from sitting in the same position for years. Unfortunately, replacing them is a real pain. You can try and soften them a little using something like MG Chemical's Rubber Renew. Doing that can be a genuine pain also but it's way easier than changing the belts.
Another solution is just to forget about the counter and cut the belt that goes from the reversing roller to the first pulley. That's what I did and I don't miss the counter at all. That's a personal thing and only you know if it's OK for you.