Great point - and there are no ABET accredited automotive engineering programs. It’s not even a category in ABET. So unless it’s a MechE with electives, you’d be pigeonholing yourself - well you would be anyway.
There are 3 ABET accredited Automotive Engineering Tech programs in the US - Ferris State, Indiana State, and Minnesota State Mankato.
But OP wants small (not Clemson) and isn’t going to get into a Clemson or UIUC regardless.