1971 Cutlass Supreme w/ a 350 4bbl. Would leaving the ignition on while testing something burn out the coil in an HEI system? I know it can w/ points.

 

I don't think it would.

 

It hasn’t done anything to the coil in my HEI.

In a points distributor does the coil go bad, or just the points?

I think it’s just the switch (points) that if are in the closed position will “burn” due to the continuous current through them. In an HEI the switch is a transistor, so if it gets hot enough it could fail (heat is bad for semiconductor devices). The HEI ignition module has a decent heat sink, so it’s probably better protected than the points contacts.

 

As the others said, your HEI ignition module will be fine with the key in the run position. The HEI ignition modules aren't very resistant to heat, especially if you have a parts store cheapie. I keep a spare in my glovebox.