How do I determine whether this clutch is working and how it operates?

I just picked up an old Zephyr 20 inch cylinder mower. Upon running the engine, the cutter and roller are both permanently engaged.

There’s what appears to be a cone type clutch and I have read it also has a dog clutch although I can’t see evidence of it. Pulling the clutch cable pulls the bottom of the left hand lever (in the image) to the right but doesn’t appear to do anything to the clutch, other than bend the plate on which its fulcrum is mounted to the left, away from the clutch.

I’ve tried slackening the cable and the clutch doesn’t disengage, and I’ve tried pulling the cable really tight.

Working hypotheses is that a) the friction faces have mated together, or b) I don’t understand what’s going on.

What visible indication should the clutch in the picture give, that it is being disengaged? Should e.g. the black sleeve slide over the spindle? Should the narrower part of the cone move inside the wider part or are those fixed together?

What’s standard practice from here to diagnose and fix it?

If I were to separate the clutch from the machine and attempt to compress it in a vice, where would I apply the pressure for least risk of causing damage?

Also, does compressing the clutch engage or disengage it?

As it happens there are some better pictures of the same clutch here, although it’s called a "weighted driveshaft" there.