The information provided by PsiX is helpful and relevant, but not the piece I was missing. The missing info can be found here, which applies even though it's talking about PostgreSQL (because it's being accessed through ODBC either way). Here is the pertinent information from the link above:
If you are using a 64-bit operating system:
• Enterprise Architect
requires 32-bit ODBC drivers to connect to a repository through ODBC;
to set up the ODBC configuration on 64-bit clients, run the 32-bit
ODBC Data Source Administrator from C:\Windows\SysWOW64\odbcad32.exe
• You can quickly load the correct 32-bit ODBC Data Source
Administrator by selecting Tools | ODBC Data Sources in the
Enterprise Architect menu bar
This piece of information was, unfortunately, omitted in the instructions for setting up Enterprise Architect for MySQL. (Too bad I hadn't noticed the option under Tools previously. Some of us have to do things the hard way!) Thanks again for the info provided by PsiX. It may be just what the next person needs so I'll give it an up-vote. :-)