It looks like you are missing the contact that goes thru the steering wheel hub. Available thru Classic Parts
[Link]The part (horn button retainer)that has the keyed hole, doesn’t need to be keyed. My ‘52 looks just like yours and it can be installed as it, no key.
Nearest I can figure, later years had self canceling signals so the tab on the back of the horn button retainer and the key would be necessary in that setup. Not required on yours and mine.
