What handle and lock for sliding door with no internal mechanism?

You could try to find the original equipment manufacturer's (OEM) latching handle, or adapt a similar one to fit the door.

A loop lock could also serve as a handle, and should be simple to install.

If you don't mind a separate locking mechanism, cabinet or drawer pulls might suffice. The latches on glass doors are usually flimsy, and can be defeated by lifting the door in the frame, so a separate lock is often used, anyway, such as one that clamps to the rail.

N.B. Be very careful drilling holes for the latch -- it is easy to crack the glass next to the hole!

You could do a computer search for "sliding door foot locks" which I have on my sliding doors or try "sliding patio door security locks".

This is somewhat of a tangent, but 1959 is early enough that it's possible that tempered/safety glass wasn't used in the door. (Internet says 1964 is when that requirement went into place in America.) If it's using normal window glass and someone trips and falls through the door, they could be severely injured or die. With that in mind, I recommend checking the corners of the glass insert for any markings like "tempered". If there are no markings, I would recommend at least considering replacement of the whole door.