My experience with a non-alarm TSM is:
1) The engine won't start without it.
2) It can be unplugged while the engine is running, and the engine will continue running. But you have to plug it back in to get started again. I've done this without any apparent harm.
3) The tip-over-sensor inside the TSM requires that it be mounted level, in the same general orientation as the stock setup.
4) I know how to disable the tip-over-sensor so the module can be mounted in any orientation. But, the alarm (if you have the TSSM) will not sense jiggling anymore. Disabling requires the module to be torn open, and resistors soldered inside. "Sidecar Mode", a programmable function in the TSM, somewhat de-sensatizes the tip-over-sensor (must be tipped over further), but it does not totally disable it. The attached photo shows half of the mod. I would stay away from this mod for safety reasons if at all possible (see #6).
5) There is no reason the TSM wires could not be extended so the module could be mounted somewhere else on the bike, but the module may be a bit heat sensitive.
6) I'm guessing the reason the module is required is that it is the TSM that can prevent the engie from starting when the alarm is triggered, and kills the engine when the bike tips over (so gas doesn't keep flowing from the fuel pump, causing a fire risk in a crash).
If someone knows anything else, I'd love to learn more.