Is the solenoid removable without having to drain any fluid? Thinking out loud again, so you can see physically what it's doing when you apply power. Short of that (pardon the pun) tracing the wiring system to see what else is "in line" with the solenoid. Find out what's going on there.

What's the year/mark/mod/numbers on that puppy. Maybe I can look at the schematics see if I can trace it out. Hey, it's good additional knowledge for me too!