If it's a '53 Henry J (evident by you stating you reached in the ceiling light) then something's not original as the '53 Henry J had the mirror mounted on the center windshield division bar. You may be dealing with something someone else installed and that could complicate things. Is this your '53? If so, it's not original if the mirror mounts through the headliner.
A '53 mirror mounts like this :
Even the four cylinder model '53s have a single chrome (stainless actually) bar down the center just for mounting the mirror.
Here's the earlier style, as Joe describes.
I've never had one of these out so I don't know what's under that headliner.