Wow ! That's some pretty ugly damage damage for just turn signals ! Although not high amperage , something shorted it enough to cause excessive heat from long term shorting .
The turn signal connector , as the shop manual calls it , not only has wiring distributed to your marker and turn signals , but there is current flowing through it that feeds the turn signal and hazard flashers as well , and those are fused independently on my '92 and probably similar on your '01 . You will need the correct schematics and start from that plug back to all power feed as you will have to determine the extent of the damage as well as the cause . You mentioned lock cylinder and ignition switch replacement , was there a meltdown in the old ignition switch as well ? I'm guessing there was and if the turn signal connector is mounted on the steering column close to the ignition switch , is it related ? I don't see the turn signals drawing power directly from ign. switch as it would get that from PDC or fuse box , but if the damage to column and turn signal shorting occurred close to the same time , maybe related someway. Only the correct diagram will show where to begin as whatever damaged or shorted it will have to be discovered and corrected . If you just splice on a replacement connector , your risking a repeat of the same damage . In my truck , I kept blowing a/c thermostats and had to find the short. It's wiring was bundled with the heavy gauge wiring for the blower motor resister and fan motor. As you can see , it's possible something else could cause this just because of proximity . Sorry it will take such research , I wasn't happy knowing I had to remove my whole dash for total five shorted wires , but that's what it took to repair it right. At the minimum , follow the diagram so at least you will have a plan to know how to take volt and ohm readings and where to look for shorts .
It's not much fun , sorry to tell you , but must be checked to avoid disaster ! Wishing best of luck , I know the pain this will cause as I've done this and it's work. But planned out , very accomplishable .
