Going back to the original symptom, the fuse blows with either the hazard light or with either turn signal. The same fuse also supplies voltage to the taillights, front running lights, and the tag lamp, so it's conceivable (but not likely) that something's wrong there and adding a turn signal simply goes over the current allowed by the fuse. Depends on what's added to the bike that taps into that circuit for juice.
Suppose you added a radio, intercom, or something, that used, say 7 amps, tapped to the running-light wire (which is common) but without a relay (which should not be done.) The tail-lights, running lights, and tag lamp might together need 4 or 5 amps total. (Pulling these numbers out of my ass just to illustrate.) So far no problem. But then you hit a turn signal which needs maybe 6 or 7 amps. You might now be at 18 or 19 amps, a few over the 15-amp fuse. Without the auxiliary load of 7 amps, nothing's wrong with anything and the hazards and turn signal work OK. Pure speculation, just illustrating that an unexpected auxiliary load of some kind could put the circuit over, and do so only when the extra load of the turn or hazard signals are used.
The only way to know that for sure is to see how much current goes through that fuse without the turn signals or hazard lights. If that's more than half the fuse rating then it's not actually the turn signals that are the problem.
I find that unlikely, though. I think you've stated that nothing extra is tapped into the light wiring anywhere. So, continuing:
It is a Very Bad Idea to substitute a paper clip for a fuse for troubleshooting. By doing so you remove whatever protection the circuits have against carrying more current than the wiring can tolerate. If there is a dead short somewhere, by bypassing the fuse and activating the circuit you are allowing whatever amount of current the battery can supply into those itty-bitty wires running the length of your bike, and they will get VERY hot, melt the insulation, the insulation of wires adjacent to them in the harness, and create about 30 more problems that you didn't have before.
DO NOT EVER BYPASS A FUSE!!!!!!!! FOR ANY REASON!!!! EVER!!!!!
Having voltage at the end of the circuit is meaningless. You have no idea how many amps were being pumped into the wire. A dead short is still 12 volts off of a 12 volt battery, more or less. The fact that you saw 11.89 volts implies a pretty significant drop somewhere along the line, which basically we already knew.
The connector method is a good idea, but that assumes you know where the connectors are.
As for finding the wires, look at the connectors at the switches, see which harness they go in to. Follow the branches of the harness and look at the connectors they come off of. You should be able to see the connectors that carry wires of those colors, and thus map the path they take through the bike. That will tell you which connectors to unplug for Silver Ranger's test, and should give you an idea of what part of the harness carries the wires so you can look for defects, cuts, abrasions, and piercings in the harness's housing.
