My whole alarm install is weird.It is easier if you drop the column down to adjust it for sure, but I am sure that it can be done, do they light up throughout any motion of the switch? if not then you are right either switch or wiring. As far as shielding are you talking about the insulation, it shouldn't be a shielded wire and why would an alarm install tie to it there, seems odd.
Lucky enough, my car is a detectives car and only had front flashers no light bars no nada.I really think that if it is was an adjustment thing in the switch that the lights would come one say in neutral instead of reverse or something along those lines. insulation broken could mean a number of things but maybe someone tapped into with one of those wire taps at one time, if it is a 9C1 maybe for the blink blink sh#$, not sure, where it is broken as far as insulation check to make sure that the strands inside aren't broken also.