tool box
electrical & ducttape(stickgum-foil or wrapper works great for short fuse fix)
trailer or pull pit guys---
fixaflat
good spare
portable air tank
road flares
2.5-5 ton floor jack
12v candle watt spot or snakelight
4x4 woodblocks(changing flats or jacking)
anything else ya think of please add..
We borrowed a trailer on a couple of occasions from another Scout troop for extended trips. It had the things you and others mentioned, but instead of the portable air tank, they had a 12V Coleman compressor/air pump with extra cord to reach the trailer wheels. Everything was stowed in a tool box that stayed with the trailer, and had a printed inventory that had to be checked before leaving and upon return.
In the toolbox was: A small can of PB Blaster, a small tube of grease, a set of trailer wheel bearings, and whatever tools necessary to change the bearings. Even if you don't change the bearings yourself, you have a set on Sunday afternoon when you're broken down 22 miles south of nowhere. There was also a plugging kit for punctures in a tire sidewall to at least try to limp home.
There was also a Mini Mag light, spare bulbs, fuses, a strip of emery cloth, spare electrical connectors for both trailer and towing vehicle, needle nosed pliers with wire cutter, red tape, (for emergency to cover broken tail light lens) a small roll of electrical tape, and a few pieces of heat shrink tubing.
A good pair of leather gloves, some nitrile gloves, a poncho, a tube of waterless hand cleaner, shop rags, and a gardeners kneeling pad. A very basic first aid kit, a spare padlock and keys. One of those LED lights that clips on the bill of a cap is handy when you need both hands and can't hold the light.
Fortunately, we never needed to use any of it, and hope you never do either.
Chris