This issue was discussed a couple years ago.  Rather than disassemble/clean, I just installed my backup unit (and a new trans. seal).  Now the backup is doing it.
I just wonder, what would happen if I stuck the spray nossel of a can of electronic cleaner into the solenoid drain hole (and sealed around the tube), filled the solenoid, let it soak a while, and then drain (?).

6 VOLTS/POS. GRD. NW INDIANA

If there’s a way for trans oil (90wt) to get on the solenoid internals it’s a possibility it could make it sticky especially if cold. The outer coil, if good, will continue to try to move the armature but the oil if there is any will make it stick. If you can take it off and clean it you will see any oil/dirt residue. Good luck. 

56 Vic, B'Ville 200 MPH Club Member, So Cal.

Right. Just looking for a simpler fix, to maybe avoid the effort/mess.  Guess I should bite the bullet and finally clean/install the original part.  The backup unit is working intermittently, even with everything thoroughly warmed up.
I'll also try Ted’s double-seal trick while I’m at it, though I’m not seeing any lube dripping from the solenoid now.

6 VOLTS/POS. GRD. NW INDIANA

Go figure.  Overdrive worked perfectly all day yesterday.  If the solenoid IS ‘gummed up’ with accumulated lube, enough use must eventually loosen everything up (?).  Likely doesn’t help either that the original 6V system is strained by running at night with the brights on, on a cold night after the car was sitting for months.

6 VOLTS/POS. GRD. NW INDIANA