I've come from the internet!
So opened ours, and ours was a Mark II too. I had to still cut all the bonds at the top, pray it open (which took an age), same tabs on the back of the switches through the same 3 holes.
It has 2 tiny copper contacts that sit on each plastic arm, and one big copper springy contact in the middle thats supposed to be wedged betwen the middle of the top and the center.
I took it completely apart, cleaned the contacts. cleaned out all the dust etc. and added machinists lube to where all the plastics all rub. I tested is as I was putting it together piece by piece again with a multimeter.
Note that the tiny contacts can dislodge really easy, you can probably glue them once they are returned to the right place again.
After I did all that, was stiff, but it works well now. I suspect it just plastic welded itself over time, which is why everything got stuck.