If this is only happening when the vehicle is in motion, I'd visually trace the wiring and look for a point where a wire or wire bundle is rubbing on something and has worn through the insulation.
If it doesn't exhibit the problem when it's parked, it's going to be hard to track down with a multimeter or test light. Unless you can reproduce it by gently manipulating parts of your wiring harness.
You'll want a wiring diagram and a troubleshooting tree, which will probably be in the factory service manual. Diagrams showing connector and wire bundle locations would be nice, too (and quite possibly also in the FSM). Other manuals will have less detailed information, but maybe enough to get you by.
You'll want to check the parts of the wiring you can get at without too much trouble and try and localize the fault. If it's in an an inaccessible location, it may be easier to splice in a new length of wire and route it as best you can around the bad spot. Especially if your wire of interest is in the middle of a wire bundle.
If it's a fused circuit, you should at least be able to narrow it down to which side of the fusebox the problem is on, assuming you can reproduce the short at will (don't try anything while the vehicle is in motion, you'll just win a darwin award).
If you're looking for a short, set your multimeter to continuity (ohms) and stick the probes on the wire you want to check (when the circuit is not powered). A small nonzero number means you have a connection between the probes. Check this tutorial.