I have been looking at wiring diagram to get better idea.
Are all fuses live and is the white wire to regulator should be live and black white should be live with key on.
Looks like the play is between the taper on the joint and the lower arm. If the arm is worn the nut bottoms out on the taper and will never get tight.
Compare with other side and look at number of threads above nut.
Just a thought get the battery charger ready to go once back together.
How bad would it be to get rebuilt then need to wait until the next day as battery charges up.
I got cable from bike shop designed for tandem which was long enough to go from standard choke lever on centre console out to engine bay under carbs loop up to front carb and connect through to all carbs might have picture somewhere.