After I put the coil on and the light didn't go on, I disconnected the coil and put test probes in the spade coil connectors. There was no current going to the coil.
When I played with the switch and the light came on, the coil was disconnected. I put the probes back in the coil connectors and the current was now registering on the meter. Put the connectors on the coil and we're working, again. It was the flaky switch that wasn't getting current to the coil.
I think you're seeing some of the same confusing issues I dealt with. The light on the dash can only come on when the pump is energized. That happens by the plunger being pushed in to allow oil flow which is what the coil does, it adds current to the shaft which pushes the valve inward. The light can only come on when the valve is pushed in and is part of the PTO safety so that it cannot be by-passed. Your valve may have been stuck in the in position and when freed would turn off the light. I changed my switch before changing the coil and no help. Would be interesting to see how long it continues to operate without replacing the switch. I have a known working switch I'll give you if the switch turns out to be bad. But leave the current switch installed to see if or when it fails.