The trouble with lubricants on delicate equipment is that dust gets stuck in the oil and the mechanism jams up.
I no longer have one of these Video tape machines but when I needed to do maintenance on my old one I used meths - methylated spirit - denatured alcohol - and a lint free cloth.
Take care - some people have acid perspiration - if that's you your fingerprints might leave a trace of where you've touched the metalwork.
I would avoid lubricants - perhaps you might wipe your hand over your hair and pick up some natural oil and wipe the parts with your fingers if you felt lubrication was needed - but I'd err on the side of no lubrication.
YouTube has several videos about cleaning VCR machines.
Good luck...
Robert Peston
September 2014