The handbrake linkages probably hadn’t been disturbed since they left the factory and were predictably grimy and the grease was quite thick, almost waxy.
Taking the handbrake out is fairly simple in theory – undo two spring clips, take out the pins they were retaining, remove the intermediate linkage and then withdraw the handle linkage through the bulkhead from inside the car.
There are two things that can make the last stage difficult. Firstly, and most obviously, the handbrake catch needs to clear all the obstacles in it’s path. Pushing the button in is enough to achieve the majority of this.
Less obvious is the end stop. This is normally held apart by the intermediate linkage and prevents the handle linkage withdrawing too far. To remove the handle linkage these need to be closed up whilst coaxing them through the various brackets under the dash.
With the handle withdrawn cleaning and re-greasing is easy and refitting is, famously, the reverse of removal.
Of note is a hole in the side of the handle linkage, it looks like this can be used to access the pivot pin of the catch but I’ve not examined this in detail.
