Thanks everyone for the tips. Here is an update on what I did to repairing the 6403B tender.
I followed the tip of CSXJOE who reprinted an article of another poster on a different forum who used an old-style automobile flasher --- and it worked! The ring sound was normal on the very first hit but the issue I had is that the solenoid coil plunger would not return all the way so the travel distance for the bell hammer was shortened on subsequent hits, minimizing the sound effect. I couldn't find any binding on the solenoid coil mechanism, I sprayed it with electronic electrical cleaner, but it still would not return all the way to give the hammer adequate travel. So, what I did was drill a small hole in the pawl, attached one end of a spring to this hole, and the other end to the hole where the old bi-metallic switch was attached. It took several attempts of stretching the spring just right to provide the tension needed. In case you're wondering, the spring I used came from an old mechanical typewriter that I took apart many years ago for its small screws and springs. See pic and video.
As suggested by the person who first suggested using a flasher, I cut off the two pins on the flasher so it would fit under the shell of the tender, leaving just enough of a stub to solder wires to them: one to the top post of the solenoid coil, the other to the lamp wire (which is powered by the center rail pick-up roller). Not shown on the pic and video is electrical tape I placed over the flasher's contact points so it would not touch the tenders shell.
The bell works best at 12-13v but running the 1656 engine at this voltage will most likely derail at the corners. I did notice that when the engine is in neutral and humming at less than 12v, the bell did sound. It just seems it won't sound when the engine is running.
