I would need clarifications.
fact: To not have the overhaul clock ticks, and to have it being reduced, you need to have your fighter in a boat bay, hangar.
fact: a PDC with boat bay is ok for that, but can't repair a fighter if a system is damaged. A ship can.
Hypothesis: you need a ship with boat bay/hangar to repair a fighter.
Hypothesis: this ship must be at a planet with a shipyard?
How do you repair a damaged component?