[Mike51Merc]

Yes, it should "clunk", so perhaps you should bench test it. To remove the solenoid, unbolt the two bolts on the flange, pull gently and give the solenoid a quarter turn.

As you saw, there are two wires on the solenoid. One wire is for the power source and the other wire (you can ignore for now) is for momentarily killing the ignition circuit for the purpose of downshifting into "passing gear". It is NOT a ground wire, except for the fact that it grounds out the ignition coil when necessary. It's normal position is "open", so it will not react to a power source or a ground source. The solenoid is simply grounded through the case, so when you attach a power source to the right wire, and ground the case, the solenoid should throw. If it doesn't, you have a bad solenoid.

OK, so back to basics. The lever controlled by the cable has nothing to do with the gas pedal. It is a T-handle cable pull to enable/disable overdrive.
The speed control (called "governor") is what controls the OD relay, which in turn powers the big solenoid. The big solenoid upshifts and downshifts the OD gears.