I snagged the wire on my Cateye Mity 8 computer on the rack the other day and broke it mid wire. I'm going to fix it by splicing them back together. I'm worried about effects of getting the wires crossed. I'm going to take some care not to cross them, but if I do, will it cause problems? What readings should I get from it with a multi-meter?
There are a few ways you can do the magnet sensing:
Reed switch (a switch which physically closes with a magnetic field). If you swap the two wires, the sensor will work fine (i.e. it doesn't matter). You can test for this using the continuity tester mode of your multimeter (you'll have continuity if the magnet is near the sensor, and open circuit with the magnet far away).
Hall effect sensor (Generally, there are 3 wires on here: Vdd, ground and the output of the sensor). There are 3!=6 ways you can wire it (so 5 ways to mess it up). Most likely, you won't get a reading from the sensor until you get it right if you don't hook it up correctly. As noted by Chris H, if you have a Hall effect sensor, chances are the wires will be color coded so you'll figure out Vdd and ground, and the remainder is output. Your multimeter won't really help you here.
An inductor (basically, a coil of wire). If you swap the two wires, the sensor would work fine (it'd be equivalent to moving the sensor to the other side of the bike, i.e. it doesn't matter). Your multimeter will show continuity always, but if you have a LCR meter, you can check the inductance. If you measure resistance, you should see a few ohms.
So, basically, if you have 2 wires, chances are you can swap them without worrying and the thing should work. If you have 3, maybe you'll have to disassemble the sensor, figure out which sensor is in there and then look up the pinout (or guess based on color coding of the wires).
There are a few more types of magnetic switches, but they're unlikely to occur in this application.