[Arran]

Very likely the pushbutton mechanism needs the mixture of old grease and dirt cleaned out of it. Most of the time these have a spring loaded bar that catches the shaft of each pushbutton as it's depressed and lets go of the previous button at the same time. So either that bar is not catching or the shafts are so gummed up that they won't go all of the way in. If you are planning on restoring this set electrically I believe you will have to remove the pushbutton assembly to access some capacitors and resistors that are buried under it, that would be an ideal time to take it out and wash the mechanism down with varsol/mineral spirits, degrease, and then relubricate the appropriate parts.
Regards
Arran