Whenever I switch either standalone or steam versions of Toribash to fullscreen the mouse becomes entirely invisible.

Could be a general OS issue. Try going to Control Panel, then go to "mouse" settings (if you're in "category" view it's in "hardware and sound" under "devices and printers"), there go to "pointer options" and make sure "display pointer trails" is unticked.

I looked at it, and it's off. I haven't made any such changes either.

Fullscreens a bit of a mess, just set your resolution to match your monitors one and run the game in windowed mode.