Resent Items reverts to zero

OS X version 10.11.6, iMac Late 2009 20.5-inch.

In System Preferences > General, Recent Items shows zero. I can change it to whatever, such as 50. That modifies four preference files: com.apple.systempreferences.plist, com.apple.xpc.activity2.plist, com.apple.systempreferences.plist.Bv50Mc0 (name varies and it self-deletes in a fraction of a second - I made a screen recording to get the file name – never found later by Spotlight), and By Host > com.apple.loginwindow.2CB41E66-5662-5609-9251-8F41D704E218.plist (name varies). I can delete all but the self-deleting file, but it makes no difference. System Preferences will not even reset to default, which I remember being 10 items.

Recent Items is not shown under the Apple menu at all. Apps show "Open Recent > and greyed: "Clear Menu" only.

Disk Utility for the startup volume shows "The volume appears to be OK".

Do I need to use Pacifist to replace the System Preferences app or is there yet another preference file hidden someplace?