As I said, last year the fan started cutting out intermittently.
Jiggling the cable at the point it entered the base seemed to fix it.
I just presumed a loose connection, but didn't bother having a look inside.
This year the fan wouldn't switch on at all.
So I unscrewed the plastic bottom of the fan,
then found an inner base secured tightly with triangular socket screws.
As soon as I found the right tool and loosened them,
the light brown oily substance started seeping out.
I'd hope it wasn't toxic, but didn't want to find out.

So I stopped immediately and screwed the outer base back on.

The oil filled capacitor sounds plausible.
Are they used in new Chinese manufactured household electrical products...?
If so, could it have started leaking last year, causing the intermittent failure of the fan to spin...???