Yes it does. And, yes, the cost of a new one is really steep. But, before you go that route: check whether your current one works (with the engine running, put the car in gear, obviously applying your foot to the brake). If it attempts to move the linkage, it is working but encountering too much resistance. In this case, try cleaning and lubricating all the linkages and check whether the solenoid is allowed to move properly against the little lever it pushes against, that it is not binding.
If the solenoid does not budge, hook up a test lamp, to see whether the wiring etc may be at fault.
These solenoids are difficult to service, since they cannot be taken apart easily. You have to basically drill it open and, after done servicing (I have a document which Bob from Brisbane sent me some time ago on this procedure), weld it closed again.
I replaced mine one off an old spare engine I bought. I have also seen them offered for something like $25 at classic car fairs. You can get one at a breaker's yard for something like that or less. Chances are it will work fine.
I am pretty sure on many (automatic or airconditioned) Pagoda's this solenoid does not work properly. When you put your car in gear and/or turn on the A/C, the idle should not budge. That's how it is now on mine and I can tell you that, after a few years of experiencing what you describe, it sure is nice!