OK, I just may have figured it out: 1. the new iMac doesn’t recognize my Kensington trackball, and 2. while I was expecting MacOS 10.15 to be installed, it has MacOS 12.
If I can’t get the Kensington to work, I’ll have to dig out one of my old USB mice since right now I have to move the one that works between the two iMacs.
How annoying, and surprising. I would have assumed that a USB trackball would appear to macOS as a generic pointing device, just like a mouse.
Maybe it’s a driver issue? If you installed any Kensington drivers (maybe to access special device features), try uninstalling them. Maybe they’re getting in the way.
Some web searching shows that the KensingtonWorks software is no longer supported. They are now offering a “Kensington Konnect” app, but it requires macOS 13 (“Ventura”) or later.
Good luck with it.