Thanks for all the responses! Both lights are on my 400A (late '31 SW). But this car appears to have been assembled from a stash of whatever parts were on hand!
I was wondering about loosening the center-back screw on the one without the rim hole but was thinking I might end up with parts loose inside a light unit I still couldn't get open if loosening that screw was the wrong thing to do.
Thanks again!
Dave