Thanks guys, I got it.
There's nothing wrong with this version of Mame32Analog+, there's just something wrong with me

Performed the following and I now have mouse control:
Typed "MAME32AnalogXP.exe -cc" and Enter.
Edited the C:\mame32\mame32analogXP.ini file as such:
### Input device options ###
mouse 1
### Analog+ options ###
multiplemice 1
switchablemice 0
switchmiceaxes 1
splitmouseaxes 1
Copied the file above to the C:\MAME32\INI folder.
Now when I start a trackball game, the Tab menu has an option called "Mouse Axes"
What a bozo. I was editing the mame32.ini file all along because that was the only ini file I was seeing. I didn't know I had to go and force a mame32analogxp.ini file to be created. I figured mame32analog+ was just using the mame32.ini file because when I ran mame32analog+ it made new entries in that file.
The case is solv - ed (in honor of the Pink Panther opening this week)