A C model is going way back in my memory, haven't worked on one in some time. It has the fuse box in the engine compartment, to the right of the engine, no? Does it have a "fuel" or "ignition" relay there as well?
Like Bobcatdan said, it's most likely a weak/failing solenoid. But if you wish to do some testing, the solenoid has three wires, red, black, and white. The black is ground, we can assume it's a good ground or you wouldn't be able to "shift it to the right" and make it hold. The red wire is hot when key is on, this is the "hold" winding circuit inside the coil. Again, we can assume it's working proper as it does in fact hold the solenoid spool in when you shift the spool to the right. The white wire only has power for a few seconds, controlled by the ECU and possibly a relay at fuse panel, it powers the "pull" winding inside the solenoid. You need a helper to do this. Probe the white wire with a test light. Have helper turn on ignition switch. See if white wire is hot momentarily. If it is, solenoid is bad. If white wire is not hot, you got power issues somewhere else. I hope this helps.
