You might have the famous "chafed wire" going to the OD solenoid. When it touches ground, it usually blows the OD fuse. But it can also burn a tiny copper trace (foil conductor) on the relay pronted circuit board. If this foil is burned, no current gets to the solenoid even though the relay operates.

The first picture below shows an OD relay with this burned trace, circled. The second picture shows the same relay, repaired (the short pink wire).

Also be sure that the wiring from the push button to the relay is intact. If the insulation wears through, the conductors can intermittently touch, forcing the relay to randomly switch in and out.