Spare parts? How about plenty of toilet paper, bee sting sticks, water purification device and tablets, extra electrical wire, butt crimp joints, plenty of black tape, a good GPS with Mexico and Belize maps, a satellite cell phone. There are actual personal distress signal devices that can be activated if caught in an emergency situation. They send lat/long coordinates to whichever service is monitoring the device. These devices are required on some mountain climbing expeditions.
It may seem like a bit of overkill, but that's why I drive a 3/4 ton Duramax as a TV.
Sounds like a great trip! Here's a link to some Belize stuff:
MayaBelize: Welcome to MayaBelize! Travel to Belize - Travel, health, weather, accommodations, activities, vacation ideas, Mayan ruins and temples, Xibalba, and much more! A satellite computer link up would let us "see" your trip.