Many types of engineers are involved in automotive design and manufacturing, and their tasks overlap with many industries.
Structural engineers optimize the body design, and can as easily move to a job in aircraft manufacture or even high-rise and bridge design.
Mechanical engineering is the most general field. They specialize in thermal sciences (heat transfer, fluid flow, combustion), which overlaps with chemical engineering, but also work on structures and mechanical design, electronics in instrumentation and control systems, and electrical power components (motors, generators, …).
There are special Manufacturing Engineers, Automotive Engineers, and Industrial Engineers which overlaps with MBA subjects.
Many Thai's have degrees in these engineering fields, Automakers in Thailand employ thousands of them !