If the rear cable to right isn't moving then unlikely the one to the left is but compare with image below showing the essence of balance mechanism from main cable.

[Linked Image]

If nothing looks amiss it does look like the issue is at handbrake lever end. If you can gain access underneath, ideally with car on ramp then compare with diagram below.

[Linked Image]

Likely issues are cable broken, clevis given way or even lever pivot bolt missing.

Richard

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