Dave this is a screenshot of handbrake system taken from 2014 on parts catalogue. I doubt it's changed much over the years. You can see that the push button (3) screws onto long threaded rod (5) and operates pawl (8) against spring (26). Maybe this will help in diagnosing what has gone wrong and how it can be corrected.

[Linked Image]

Richard

2018 Roadster 3.7
1966 Land Rover S2a 88
2024 Royal Enfield Guerrilla 450
1945 Guzzi Airone