Does the ARcGIS Service Account have permissions to the MySQL Database?
Which user are you using to create the ODBC Connections?
I never set up any permissions in mysql. I used the same user for everything.
If you open the 32 and 64 bit ODBC panels side by side, and create one in the 32 bit user DSN, it will show up in the 64 bit user DSN, but you still have to add one to the 64 bit with the same exact name, description, and connection properties as you did for the 32 bit.
After I did that I quit getting the general function failure.
I was able to link MySQL tables to Desktop 10.0, but not 10.2.2. ESRI Customer Care told me in Feb. 2015 that it was no longer possible with 10.2.2. https://community.esri.com/thread/10539 However, I haven't tried the 32 bit MySQL ODBC drivers with 10.2.2. On a Windows 7 64 bit system, there is a executable that allows us to set up connections with the 32 bit drivers at C:\Windows\SysWOW64\odbcad32.exe.
Dang! It works to use the 32 bit user DSNs to MySQL 5.1 data sources, same as it did for me under Desktop 10.0! A period appears in front of all my table names.