Brake socket question

It looks like I have to replace one of the brake sockets on my 1978 Ford Granada. When I apply the brakes, only one filament of the bulb lights.
The brake filament doesn't turn on at all. There are three wires going to the socket. The wires are cappped with crimped wire connectors. Can these connectors be removed by just pulling them out or do they require an extractor? Are sockets normally replaced by cutting the existing Ford wires and connecting the wires of the new socket onto the existing wires?
Thanks in advance
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website by car enthusiasts for car enthusiasts. It is not affiliated with any of the car or spare part manufacturers or car dealers discussed here. All logos and trade names are the property of their respective owners.