I set aside some time to troubleshoot the tractor today. Thanks for the help and suggestions!
CIHTECH, both halves of the lockout switch look clean and I think it's functioning properly. The moving half rotates down and lines up with the stationary half only when I shift into 4th range. If I do this while in reverse, the tractor doesn't move when the clutch is released, but I noticed that the "shift to N" light doesn't come on. Anything else to check on this switch?
I measured the resistance on all three solenoid coils on the shuttle, and they are in the 9.3-9.6ohm range. Some insulation is broken off the diff lock solenoid wires, but the wires are all intact and not making contact with anything they shouldn't be.
I disconnected the forward and reverse solenoids and checked for battery voltage at the plugs. With the selector in forward I measured about 12.5V at the forward plug and 40-60mV (essentially nothing, I assumed just noise) at the reverse plug. These voltages were flip flopped with the selector in reverse.
I then drove the tractor in reverse until it dropped out of gear and the "shift to N" light came on. I left the selector in reverse but took the tractor out of gear and range. At that point there was no voltage at the reverse plug. Moving the selector to neutral and back to reverse restored the 12.5V to the reverse plug.
I then swapped the plugs on the forward and reverse solenoids. So putting the selector in forward drives the tractor in reverse, and vice-versa. In this scenario, with the selector in forward the tractor drives in reverse with no problems. I tried different ranges (not 4th), gears, starts & stops but couldn't make it drop out of gear. However, when I put the selector in reverse to drive the tractor forward it would drop out of gear frequently and the "shift to N" light came on.
Seems to me this is some kind of electrical problem, but not sure what to check next. Any more ideas or suggestions?