Lyall has a good point. Make sure that the wire running from the switch to the connector is hot with 12 volts positive when the switch is on. If that is true, make sure that the other terminal is grounded well to a bolt. You should be able to measure 12 volts across both terminals on that connector.
Old mowers are prone to having electric grounding problems.
My JD 318 pto quit about a week ago. I thought the switch was bad and bought a new one.
It is on a shelf in the garage. should have checked wiring first. found loose wire in a connector. I fixed that and it is working fine now.
Your getting good advice
I forgot to add last night that you may need to check the air gap on the clutch. Being electromagnetic if the gap is too much the coil may not be strong enough to engage. I do not know what the air gap is on a MF,so check the specs. On a JD 318
it is .014-.018.