This pinky switch doesn't show up as a button in game until you change it in the software.
The software to program this stick is a PITA to use. There are actually 2 programs, "Wizzo" and "VKB Device Configuration Software (VKBdevCfg)". To get this thing working, I had to use the second one - VKBdevCfg - because the 1st one kept crashing. It is nothing resembling user friendly, so here is how to set that pinky button:
Run it and get this screen:

From that confusing screen, the "sS7" under "Line 7" is what you're looking for. Click it and get this screen:

Change the setting to match what is in the image and you're set. Note, through, that the little mode switch on the base effects this button. So if you change modes on the stick, it screws up the views in AH. Remember to click "Set" at the top to write the changes to the stick memory.
Thanks to everyone that tried to help me last night.