Thanks for all the help. I'm way out over my ski tips on this one. . .
I tried a backup and copied the log. It is quite long, so tried to paste below where it appears to start to go wrong. I've removed the name of my computer and replaced with XXXXXXX. Otherwise this is exactly as it appears. I'm going to try the other steps this weekend, but wondering if any of the following sheds light on the issue:
2021-09-09 21:37:04 Cached event database was unreachable at /Volumes/My Book for Mac/Backups.backupdb/XXXXXXX iMac (79)/2021-09-09-213658.inProgress/C309C9CB-6C9A-4A34-933E-01F603BB81A8/.87EB482A-B6F5-3F9A-9C2A-FD1E652BE9C9.eventdb
2021-09-09 21:37:04 Possible strategies for "Macintosh HD - Data" (device: /dev/disk2s1 mount: '/System/Volumes/Data' fsUUID: 87EB482A-B6F5-3F9A-9C2A-FD1E652BE9C9 eventDBUUID: E59C3A04-F682-4779-BB78-0AD01E37922B) (<EventMarker 2021-09-06 20:59:35 +0000 75743201 E59C3A04-F682-4779-BB78-0AD01E37922B 0>): first backup, deep scan, FSEvents,
2021-09-09 21:37:04 Using FSEvents for source: "Macintosh HD - Data" (device: /dev/disk2s1 mount: '/System/Volumes/Data' fsUUID: 87EB482A-B6F5-3F9A-9C2A-FD1E652BE9C9 eventDBUUID: E59C3A04-F682-4779-BB78-0AD01E37922B)
2021-09-09 21:37:04 Read 0 clone families from /Volumes/My Book for Mac/Backups.backupdb/XXXXXXX iMac (79)/2021-09-06-174437/.87EB482A-B6F5-3F9A-9C2A-FD1E652BE9C9.clonedb
2021-09-09 21:37:04 Buffering events...
2021-09-09 21:37:04 Unrecoverable zero fileid - path: 'Users/XXXXXXX/Library/Containers/com.apple.Safari/Data/Library/Caches/com.apple.Safari/WebKitCache/Version 16/Blobs/97829D2F9B149F4B0DBD93B1D000E22F51831C81', flags: 00100200
2021-09-09 21:37:04 Event collection stopped because of error: Error Domain=com.apple.backupd.ErrorDomain Code=303 "(null)"
2021-09-09 21:37:04 Failed to collect events for "Macintosh HD - Data" (device: /dev/disk2s1 mount: '/System/Volumes/Data' fsUUID: 87EB482A-B6F5-3F9A-9C2A-FD1E652BE9C9 eventDBUUID: E59C3A04-F682-4779-BB78-0AD01E37922B), error Error Domain=com.apple.backupd.ErrorDomain Code=303 "(null)" UserInfo={FailedStrategy=16}
2021-09-09 21:37:07 Unmounted local snapshot: com.apple.TimeMachine.2021-09-09-213702.local at path: /Volumes/com.apple.TimeMachine.localsnapshots/Backups.backupdb/XXXXXXX iMac (79)/2021-09-09-213702/Macintosh HD - Data source: Macintosh HD - Data
2021-09-09 21:37:07 Mountpoint '/Volumes/My Book for Mac' is still valid
2021-09-09 21:37:07 Mountpoint '/System/Volumes/Data' is still valid
2021-09-09 21:37:07 Backup failed (303: BACKUP_FAILED_PREFLIGHT_STAGE_GATHER_EVENTS)
Any thoughts are greatly appreciated.
Thanks.