Apparently there is an issue with FileMaker installations.  Filemaker ends up borking the Windows Registry so that later installed ODBC Drivers don’t load.  This means when you install the MySQL ODBC Connector/Driver, it will not show up in the ODBC Driver list.
 
The issue is caused by a misplaced (default) registry value.  The easiest way to fix it is to delete the default value, as it does not need to be set.  Other’s have suggested exporting the whole key, to a .reg then deleting the key, removing the @=”" from the backed up registry file, and then re-installing the key.
 
or you can just run the following .reg file:
 

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SOFTWARE\ODBC\ODBCINST.INI\ODBC Drivers]
@=-