There are 3 sets of contacts on the PTO switch so regardless of weather you can hear the clutch throwing or not, the pto light is signalling an engaged PTO to the rest of the wiring.
So it will be lots of WD 40 ( or your favourite similar goop ) then work the switch a lot to flush out any gunk, remove & replace the plug a few times to make sure you are getting good cantact on the switch terminals.
If no joy then 99% chance the PTO switch is US