Ok. Thanks to all for your thoughts and suggestions. Here's the final result.
When I laid down on the floor (sure wish these old eyes could still focus close up!!) I touched those little white pieces and discovered that they just fall out (held by silicon grease). They are plastic and are supposed to be part of the ball valve arm. Those are what meshed into the slot at the end of the pedal shaft. They are broken off.
(So now I know that my observation that there has never been a hard connection between the pedal and valve means that this has been wrong for a very long time, perhaps only the screw was loose.)
So I call Dometic Customer Support (very nice people) and asked for the part number of that ball valve, the plan being to call around and see if a local dealer near this campground had it. She gave me the part number. I then asked the nice parts person to verify that the valve comes out thru the top. She didn't know but gave me a phone number for the Sanitation department. I told that (again very nice) person what was going in and asked about removal.
She told me that the ball valve cannot be removed on this toilet. It is installed before the plastic and ceramic parts are joined together (and those are never to be split). They have to replace the toilet.
Since it's under warranty (serial number was enough to verify it was less than 2 years old) they are shipping me a new one free of charge from a Dallas warehouse. My new toilet will be delivered to the campground tomorrow!
Dometic Customer Service is TOP NOTCH!