It's by no means a 'single word', but many automobile mechanics would say that they do "Auto Repair". Though this of course only refers to the reparations of a vehicle, not the construction of one or the upgrading of one that is not broken.
For the act of working on a vehicle, there is "tuning up", or "bodywork" if you want to refer to only the outer 'body' of the car.
Or you could modify the two, since both individuals are engineers.
You could try 'automotive engineering' or 'electrical engineering', but both of these phrases specifically refer to automotive engineers and electrical engineers, rather than mechanics and electricians, so to avoid confusion, this is only advised if the person's role is already well established by context.