It may not be that feature if you can't even manually lower the glass the rest of the way with the button. It seems odd that the glass won't fully lower and maybe another early JS Convertible for comparison could answer this question better.
There are mechanical downstops and upstops inside the door that are adjustable. It would be strange that they are out of adjustment unless the doors were apart in the past and why both front doors? I'll look into this more if I can.