I would add that if possible, the multimeter should be able to measure at least 10 amps, and preferably more, though they tend to get expensive when they can measure that much amperage. If not, you can buy a Panel Mount Amp Meter (from someplace like www.allelectronics.com) for about 15 or 20 bucks, and just use that.
Also, a lighter. You use the lighter to shrink heat shrink tubing, though there are better or other ways, a lighter is pretty easy, cheap, and easily replacable.
A small socket wrench, with extensions. You may not need a bunch of sizes, since 10mm seems to be a very common size that one works with on a car, I would get at least a set with 14 mm being the biggest, going down to at least 4 or 6 mm.