The basis for the jet car was a Ford F-350 pick-up. I'm not sure of the model year, but since product placement was presumably a consideration, it may have been circa the movie's 1984 release.
According to Carl Dowds - I believe that it is a 1982 Ford F-series pickup truck, based on the grill assembly, Ford grill logo, and windshield shape."
Other brand name components included Goodyear tires and Monroe shock absorbers. The frame assembly was reinforced, including adding the front end from a Grand National stock car. Other additions included air scoops from a DC-3 transport plane, the cockpit from a World War II German fighter plane, and parachute packs to assist deceleration. Engine modifications included an oversized carburetor and making room for nitrous oxide tanks for extra speed. As for the jet engine itself, in addition to providing a visually impressive trail of flame and smoke, it's capable of producing 3,000-4,000 lbs. of thrust, which translates to speeds of 150-200 mph for the jet car. This is well below the mach-plus speeds it's said to reach in the story, but it's still pretty darned impressive for a "movie prop"!
According to M. Mitchell Marmel :
Interesting note vis-a-vis the turbine engine used in the film: It was a Cold War-era GE turbojet that was loaned to the production by Northrop University in Inglewood, CA. I helped push the jet onto the truck that one of the Northrop students (who arranged the deal, and whose name eludes me) used to pick it up. When I asked what the jet was for, he said, "Someone wants to put it on a pickup truck for a movie!" I snickered and thought nothing more about it until September of 1984, when I caught "Buckaroo Banzai" in a Pasadena movie theater. I thought, "H'm. That engine looks familiar...HEY!" Had I only known, I would have insisted on going along to the location shoot...
Finally, personal touches were added to reinforce the impression that the jet car had been personally crafted by Buckaroo and his team. Interior decorations included a dashboard hula dancer and a worn picture of Buckaroo's parents (portrayed by James Saito and Jamie Lee Curtis).