(Honestly wondering about these 2006 Vulcan 900s if something was just not right in the design this first year. Maybe I should fix and sell....)
Naw.....it's a great bike.
Seems as though a LOT of metric bike makers undersized the connectors for the stator.
Then just the tiniest bit of loosness and it heats up ....more and more as time goes along until melt down.
Exactly how you go about testing and repairing depends on your skill with a soldering iron.
A wire nut is a good temporary option if there is enough slack in the wires.
Even a bolt or alligator clip should work for a quick test.
Of course, the burnt wires will need to be scraped clean first.
If that looks good, do all 3 of them.
Might have been a good idea to solder them after you knew you had a good stator but hopefully no harm is done beyond the wires.