OK, I figured it out.....
I did not have the "Joystick enabled" option selected. Once I enabled this option then Mame automatically recognized my left/right pot. I did not even have to (or was even allowed to ... for that matter) set the "AD Stick X" setting manually. This seems to be because the left/right pot was the only Xaxis pot connected at the time so Mame simply uses that one to be "AD Stick X". Anyway, when I connected my throttle Y-axis pot, then Mame automatically used this pot for the "AD Stick Y" setting. I still did not have to (or was even allowed to ... for that matter) set the "AD stick Y" setting myself since the throttle pot was the only "Y-axis" pot connected.
However, when I connected my second Dual Strike (this is where the brake pot Y-axis was connected), then Mame must have recognized there was now 2 Y-axis pots connected and then allowed me to specify which Y-axis pot (throttle or brake) to use for the "AD Stick Y" and "AD stick Y2 settings.
My original problem (causing me to open this thread) was because I was only connecting one pot at a time to test whether Mame would allow me to assign a pot to a particular "AD Stick X" or "AD Stick Y" setting. But since Mame does not allow manual configuration of the "AD Stick" settings when only one pot is connected of a particular axis type, then I thought I was not doing something correctly. I thought my HangOn assembly was not being recognized......
Anyway, the world is now good once again and I can continue wiring up my driving cab ....