I’d pull the lowers and see if the damper oil has passed the seals into the lowers.
^ I’d put (a small amount) money on it being that…
Not unusual on an older fork that’s been sitting, seal gets sticky and adheres to the shaft, and then when put back into action micro-tears/rubs and shortly after pisses oil into the lower.
Very easy to check by dropping the lowers though, if you’re not immediately covered in oil from that leg then you’re still in a good position to diagnose further by confirming which leg is the issue, and then investigating further from there.
Good news is if it’s that seal it’s a dead simple fix, replace that seal. Even better news is that that seal on it’s own costs about 50p. Bad news is I can’t remember the exact dimensions, but the full seal kits should be relatively cheap though and you might as well do the others while you’re at it.