external drive not showing in disk utility?

There can be any of several reasons:

• The disk may have failed (this can be ruled out if the disk works with other Macs)
• The disk may be formatted in a way, or with manufacturer firmware, that is not compatible with Monterey. To avoid this, only use Disk Utility to format disks. Use of manufacturer disk firmware or utilities for encryption, security etc. runs the risk of incompatibility with the MacOS when it is updated/upgraded.
• The disk cable may be bad (can replace it to test)
• Some docks or hubs are not compatible with Monterey

You did not provide any info pertaining to any of the above so it's not possible to tell if any of these possibilities might apply to your situation.

Make sure you select the drop down menu item in Disk Utility to "view all devices" as unless you do that, the device might not show up in Disk Utility (it would be there but hidden until you specify show all devices).

Tehawk7 wrote:

Thank you very much Steve. the reasons above are ruled out and 'view all devices' is selected.

Maybe the problem was caused by also using that disk on my other Mac mini from 2012 running El Capitan?

At one point previously Disk Utility stated that it tried, but could not repair the disk and said I could not change anything on it, but that I should try to copy the disk to another disk and then reformat it. I regret not doing that when I had the chance. Instead I tried it on the other machine and it would not mount.

What you describe is consistent with the disk having failed. One sign of failure is that the Mac suddenly states that the drive is read-only and warning to copy all files from it as soon as possible. A second sign of failure is for the disk fail to mount, for instance after being dismounted and then refusing to mount on the same or some other computer. I have seen both of these symptoms with external drives that have failed.

If the drive is formatted as HFS+ it should mount immediately with full functionality on Macs running El Capitan as well as later MacOS (including Monterey). If it formatted as APFS, it won't be recognized by El Capitan or Sierra and won't mount on those computers. If it has been formatted using some other third party utility not Apple Disk Utility, it might fail to mount under Monterey (even if the disk is healthy) if the third party software was at a version not compatible with Monterey. If the drive has been formatted to be usable on both MacOS and under Windows, the software/firmware used for that often requires an update to work with Monterey.

So trying different Macs is not a bad thing, especially if the drive is marginal and might work with one Mac but not with another. But becoming read-only and then refusing to mount is a sign of drive failure. Once it refuses to mount, there is almost no way to recover anything. I have had drives that refused to mount but after repeated tries did mount, but even then attempts to copy files resulted in various error messages and did not succeed.

Hopefully you have a backup of the external drive. If it is HFS+, in addition to Disk Utility (which you tried already), you could try other tools like Disk Warrior or Disk Drill to try to recover it. It sounds like a physical failure has happened, however, in which case these different utilities are not likely to work.

If you go to About this Mac>Overview>System Report>Hardware>USB (or Thunderbolt depending upon connection on disk). Is the drive listed? If the physical drive failed the disk will still be identified. If the enclosure electrons failed it will not be identified