I think you only have to use the victim, after the kidnapper is dead. No skill necessary.
Instead, if you use medical skills on the victim, you will certainly mess up and fail. Why? I think it's because it overwrites the use of STC VICTIM-1 but did not overwrite the clue.
When I fail, the mayor only says "All is lost". When I succeed, the mayor gives me the reward. Whatever the case, the quest is stuck in my memo.
I remember in earlier version of Gearhead, it is possible to be too late for the victim at the scene after you go thorugh all those tidious tracking. I guess the difficulty is tuned down a bit, but the quest becomes buggy.