Recover access to iMac

Connect a USB keyboard.

If either of the Apple Bluetooth keyboards is rechargeable, connect the Lightning cable used to charge the keyboard into the Mac, and try again.

(You might need “the other” Lightning to USB-A or Lightning to USB-C cable, depending on which cable and the USB ports on whichever iMac you have.)

Interference from other wireless devices can aggravate the issue:

Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support

With my 2017 iMac, the keyboard, mouse and Magic trackpad can all lose connection at the same time if I place my iPhone too close to the keyboard tray that the there devices share.

My older Macbook Pro shows a similar response to the iPhone being too close. It uses a different Apple wireless keyboard and mouse.

ralphbrau wrote:

BINGO! The cable restored access! Many thanks!

Next question: Is this likely to be a "one off" event, or does it indicate a developing failure of some kind? (I keep TimeMachine backups, but they are encrypted and may not be useful if the iMac fails.)

🤷‍♀️ Bluetooth, Wi-Fi, and keyboards can all have transient glitches, and old iMacs can develop less-than-transient hardware issues.

I usually run with the Apple recharge wireless keyboards and trackpads wired. I have the USB ports available, and don’t mind the wires.

Time Machine backups should be fine for recovery, so long as you remember the password. Enabling iCloud Keychain or using Keychain secure notes or other such can help, there.

I usually run parallel TM archives, as TM does occasionally glitch, HDDs can fail, and the power can drop out at an inopportune moment, etc.