I recently completed a lighting upgrade to my small garage as I previously had lights over my bench as well as a retractable light for working under the hood, but I had no lighting directly over the car. I solved the problem with about $100 and the better part of a day. Maybe my solution can work for your space too. I ised some scrap PVC and some black iron from the home center to make a pivoting arm that I mounted a LED shop light to. I used a scrap piece of 1.5” PVC pipe and cut and epoxied a longitudinal “spine” to the pipe that I fashioned from some flat PVC trim stock. I drilled hole in one end to accomodate the black iron pipe, collar and end cap. I was able to mount the fixture on a beam the runs through the garage and I plugged the light into an existing outlet that had been used for an old garage door opener. The best part is that the light I got has built in bluetooth speakers so I can listen to tunes while working away in the garage.
Zip tied the cord to the black iron pipe.


The black iron keeps the unit rigid amd because of the spine on the horizontal pipe, the unit flexes very little when the power cord is pulled


The light itself was only $59 at HD and is very light so there is no strain on the joint between the PVC and black iron.


The fixture can swivel 360 degrees so I can concentrate light on any side of the car


Clears the garage door as well so I can listen to my music while washing the car in the driveway

Nice!