Thanks for the responses. Yes lostarchitect, it looks exactly like that. So, there should be a bold through the hanger that threads into a nut which locks it in place in the hanger. That bolt and nut were missing on the original bike as I found it. It had a non-quick release and the nuts on the axle were just tightened down to hold the hanger in place. It worked unless you ever needed to remove the wheel.
That means the other side has to be adjusted such that the wheel doesn't slide all the way back to the end of the hanger with the stops in the pic from ex pres?
Looks like I'll need to go in search of a few replacement parts. The other old steel framed road bike I have was exactly the same - missing the nut/bolt and stop for the other side.
I wonder why they built them that way. Seems complicated when it could be pretty simple. And it leaves a lot parts that could shift and misalign the rear wheel.