Mouse and Multi-Mouse are enabled. Even then, I can't get MAME to see the touchscreen's inputs as valid.
Any other ideas?

Edit:
Messed with it more. Apparently the touchscreen is not a mouse. It's a GUN. It shows up as a Lightgun, and started working once I enabled it.
What's weird is that in Touchmaster it doesn't track tapping very well, despite touch to click working fine in the OS. I tend to have to double-tap to get it to register a touch. This may be the Touchscreen > Mouse translation's problem, though, not MAME's fault.
I also noticed that the "Lightgun" does not translate from the 16:9 panel to a 4:3 image on screen. I think this is the same problem the lightgun guys have. I think they have to actually run and calibrate the screen in 4:3 in order to get proper tracking. I'd really like to avoid that if at all possible.