Old washing machine takes long and longer to do a cycle
If moving the programmer forward a notch fixes it, it's most likely simply a failing stepper-motor on the programmer. I've fixed a similar vintage machine with a similar fault.
It's not terribly hard to fix, but the programmer can be fiddly to disassemble (in a &quot;re-assemble-able&quot; manner) because they have lots of gears. If you can get to the end-shafts of the steppers you can see which is failing by attaching a 'flag' or marking it, to see which isn't moving.
I believe these items are fairly generic; When mine failed, I went into our local appliance-repair store with the old one in my hand, not really expecting that they would have one, and would have to order it in. I'd barely opened my mouth, when the guy at the counter reached behind him without really looking and put a new one on the counter!
Obviously, the usual caveats apply; be careful when operating the machine with exposed mains, and rotating parts which can trap unwary fingers. It goes without saying that it should be unplugged before any repairs are attempted.