Toshiba external hard drive won't mount, is not visible in Finder / Disk Utility

The vast majority of the time it's the USB cable that has gone bad. That's the first thing you would want to try and replace. You'd also want to verify it on another computer, though if the drive is Mac-specific formatted you'd want to try it ONLY another Mac (such as a Mac at an Apple store if you don't have access to another one through friends/family/school/work (not a Windows PC).

If it's not the cable/computer/ports then it's most likely the external enclosure itself. If the drive is out of warranty (or if the primary concern is your data already on there) you can transfer the drive within the enclosure itself to a new generic SATA external enclosure. Those cost about $20.

Try using a powered USB hub from a reputable manufacturer. The hub will supply any extra power the hard drive may need and it can help buffer the USB connection.

Can’t be seen in either Finder window or Disk Utility.

Have also tried it on an older MacBook & a PC, no joy there either.

You've tried a new adaptor but have you tried a new cable and different port? Do you hear the drive spin up when it's turned on?

Did the drive come with software? Did you install the software?

Why don't you call Toshiba customer service for help this is their phone number 1-800-457-777. Explain your problem(s) that you are having.