Hi Derek and welcome to Beoworld!
I did it on my Beogram 4000 and 4002, which were completely stuck.
Basically, you have to remove the lid, then open the deck (see here), remove the arm cap and unscrew the left part (two screws), which bears the arm lift along with the detector arm. Be careful, the wires are kind of fragile!
Then you need to remove the circlip (you'll need a special tool, not expensive), pull out the moving arm (careful, it's hard and can come out all of a sudden, plus there's a spring which always wants to jump somewhere and live its own life... never to be seen again!), clean everything and put the thing back into place after a drop of fresh oil!
Do the same thing with the horizontal lever, at the base of the arm (circlip, etc.).
Not for the faint-hearted but provided you can handle mechanics I'm sure it'll be fine. Make sure you re-align the detector arm correctly.
Good luck!