Apple Wireless keyboard (AA batteries) "ghost in the machine"

That's a new one. Some considerations:

1) Remove the batteries, allow the board to sit without them and then reinstall, preferable using fresh batteries.

2) Although a long shot, you can also try an SMC reset on the computer in case something in the management controller that handles Bluetooth is acting out. instructions here:

How to reset the SMC of your Mac - Apple Support

[NOTE: You computer does not have the T2 security ship mentioned at the top of the article,so skip that part.]

3) Also see this article on interference with wireless signals:

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

There is a decent chance that some other device on or near your workstation—a phone, wireless printer, wireless speakers, etc— is interfering with the signals between the board and your Mac.

jackbootthug Said:

"Apple Wireless keyboard (AA batteries) 'ghost in the machine'"

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Bluetooth Module:

Try the following user tip: Use "Reset the Bluetooth module" to Fix Constant Bluetooth Disconnections - User Tip