I like molykote 33 for this sort of stuff if there are plastic parts in there.
Less is more it seems, if it hasn't migrated to the electrical section before, why would it now?
There are no plastic parts except for the casing. It's 25 years old (which is probably a good thing) and appears to be quite well built.
I've had another look at the division between the 2 sections and it looks better than I had originally thought. There has been some seepage but it's toward the bottom and away from the electrical.
As my plan A, I think I'll try to spread out the old grease, as suggested by wayne50. There might be just enough.
But any further suggestions on a replacement grease would be welcome.