Dave. The chime hasn't worked in decades. I can't see a striker or anything that would enable the chime to sound. Is there a separate mechanism that strikes the bell? Post a photo if you have one. In the diagram you posted, I don't see any mechanism that would chime.
In the solenoid and selector photo I posted part of the switch is broken as you pointed out. Is this where the chime strike would be located?
It's a bit hard to see in the diagram, but the striker is part 54157 / 52690. It would be a piece of metal (I think just a basic screw?) on the end of either a short piece of flexible wire or plastic.
If you have the space and electrical capacity, you should hook both dryers up! One washer with two dryers is a very favorable combination due to the imbalance of time it takes to wash and dry.
Dave,
Previously, I couldn't understand how the chime mechanism operated. Enlarging the photo once again and from your description, I can only quote Ernest Hemingway. Thank you!
I hope you can see the link.