Unable to unpair Kensington wireless mouse

Ok, a iMac 12.,1 would be a 21.5" Mid 2011 model.

Am I correct to assume that the Kensington mouse was purchased around that same time? Are you sure that this mouse must be unpaired BEFORE it can be paired with another Mac?

Since this mouse doesn’t appear in the Bluetooth list on your iMac, that actually tells us something useful: the iMac is not currently paired to it. High Sierra shows all paired devices—even if they’re offline—so if the mouse isn’t listed at all, it’s almost certainly not bound to that Mac anymore. In other words, there’s nothing left to “unpair,” and the mouse should be free to pair with another Mac as long as it’s put into its pairing mode correctly.

As far as pairing it with your Mac laptop (again it would be helpful if you can provide both its model number and operating system version), the more likely problem is that the mouse is either (1) still trying to reconnect to some other computer it was previously paired with, or (2) not actually entering pairing mode. Many Kensington models require holding the power switch in a specific direction for a few seconds, or pressing a small connect button on the underside. If that step isn’t done precisely, the mouse just wakes normally and never advertises itself to the new Mac.

Here's what I suggest that you try:

1. Turn off Bluetooth on the iMac entirely (System Preferences → Bluetooth → Off). This prevents the mouse from bonding with it even by accident.
2. Power-cycle the mouse, then hold its pairing button or pairing gesture long enough for the LED to flash (often 3–5 seconds). Note: I'm just guessing here as I don't know which mouse model you have.
3. On the new Mac, open the Bluetooth settings and wait 10–15 seconds. Kensington mice often take a moment before they appear.
4. If it still doesn’t show, try pairing the mouse with any other device (even an iPad or another Mac temporarily). If that also doesn’t see it, then we’re dealing with a mouse-side pairing-mode issue or a depleted battery.

The image you provided is not a Mac running macOS 26.1, but a much older version of macOS or OS X. Can you please clarify both the exact model of your iMac, and its operating system version, that you are currently using this mouse with?

Have you also contacted Kensington support to see if they can assist you with this as well?