The "spare" black wire is the one that is supposed to provide the 12V input to the kill switch. The black/white is the output of the kill switch. Connect the black wire to a black harness wire, and measure the voltage on the disconnected blk/wht switch wire, with the key on and the kill on; it should be 12V with the kill on, and nothing with the kill off. If so, turn the key off, reconnect the blk/wht wire, and turn the key on and kill on. See if the fuse blows. If not, test for spark. If the fuse blows, report back.
BTW, your meter is set in the 20K-ohm position; this is for testing large resistances like 10,000 ohm spark plug caps. For low resistance readings, it should be set to the lowest level of 200 ohms.