Okay, here's some thoughts.
First, Gruffle, the difference between Engineer and Mechanic is that an Engineer has sufficient education to design and develop new inventions based on that skill. Consider the difference between a grease monkey at a mechanics shop...and the guy who designed and built the engine in the first place. Said grease monkey can keep it running. He can take it apart and put it together again. But he can't really analyze the design (beyond "this model seems like it always breaks on the pinion joints!" type observations), nor could he design an entirely new engine.
GURPS Engineers (perhaps unrealistically) can not only service and repair the subjects of their skills, but can gain detailed technical understanding of them by studying them, or schematics. They can attempt to design improvements and implement them. Engineering can do anything Mechanics can do, and more.
Additionally, there's no such skill as Mechanics (Jump Drive). You -have- to have Engineering, because that skill is required to plot the jump, as well as maintain and repair the drive.
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Now, as for the ship...
I suggest that you and I link our backgrounds somehow. Then both our characters have a stake in the ship. This would probably happen anyway, because a ship needs, at minimum, two skills to run it. A pilot, and a jump engineer. Sometimes, like with single-operator Scout Service ships, those can both be done by one person, but that's uncommon.
So for example...
What if my character's father, who is an asteroid prospector (a 'belter') has associations with your character somehow. Perhaps professional, perhaps personal...friend of the family...you saved his life...whatever. Now his big find is a derelict starship, which under right of salvage is now his. He's planning on selling it and retiring, but there's an accident of some kind that leads to his demise. The ship is in his will to the two most important people he had left at the time...my character, and yours.
It would have taken time and money to refurbish it and get it spaceworthy again, but we decided to do exactly that, even though we could have gotten a goodly chunk of change by just selling off the hulk.
The precise nature of the ship is of course, up to the GM...though it shouldn't be anything obviously special, since the Imperium would have confiscated something like that.
