I have not heard that common phrase in many years:
Grease Monkey. Some of my best friends have been or are Grease Monkeys. Not me. I don’t have the brains for mechanics.
Gearheads?
I love to do engines, but I dont have the patience or the eye for bodywork. Those guys are artists.
One of the smartest persons I have ever known was a mechanic, had a college degree in business. Made a good living and raised five kids being a mechanic.
The more modern term is “gearhead”.