Mac – SSD in external usb 3.0 case not recognized

I use a USB 2.0 external hard drive for Time Machine, and I have not seen any changes in speed. Time Machine works pretty quietly and effortlessly in the background without slowing down the Mac's performance. According to the Time Machine System Preferences pane,

Time Machine keeps:

• Hourly backups for the past 24 hours
• Daily backups for the past month
• Weekly backups for all previous months

The oldest backups are deleted when your disk becomes full.

It seems like, since the SSD is not recognized at all, and:

• The USB ports fully function
• The SSD fully functions (with older Macs and Windows computers),

the only conclusion to come to is that the adapter uses drivers which are not present in newer MacBooks. Even if the old and new MacBooks are on the latest version of macOS (Sierra as of writing this), there is some connection between the adapter and the hardware you are trying it on.

Solution: use a different adapter (this solved my problem!)

Many thanks to Allan for his help resolving this issue. This answer has been posted with a different account by has been written by the same person who posted the above post (I lost access to that account somehow.) Likewise I can't choose this as the answer to the question, but if Allan sees this and writes his own answer, I will delete this one and vote him up. (I can't ping him as I have <50 rep)