I am not familiar with those error messages. You didn't happen to change from 32-bit JMP in JMP 11, to 64-bit in JMP 12, did you? If so, you would have a driver bitness mismatch that would prevent JMP from working with the Access ODBC driver.
The ODBC driver error is:
[Microsoft][ODBC Microsoft Access Driver] Cannot open a database created with a previous version of your application.
This is what I found from Microsoft.
“By design, recent versions of Access cannot convert Access 97 files.” this is an unfortunate comment in the doc.
It looks like a file format change.
I little more info is here: