The rules say each Minecraft action can only have one input and each input can only cause one Minecraft action, but since you can't change the keybinding of F3 in Minecraft settings, would it be against the rules to find F3 to one of my mouse side buttons? (The F3 key and the mouse side button would both cause F3 to come up)

@yangers I wouldn't imagine it would cause trouble, but create a support ticket or contact one of the Mods first.

@Mortysmith if you go in your mouse driver settings you can rebind f3 to another key

Yeah you can't rebind it in game, but according to the rules:

You may remap keys using external programs, but

Each game input may have only one key, and each key may cause only one game input
Inputs must be buttons - no scrolling the scroll-wheel or similar

So yes, you can remap f3 to your mouse button, but you're not allowed to remap F3 + esc or things like that to one button.