Welcome.This is a new resource but with a few,"Old Hands".We know most of the things about CX/GLs between us and there's always something to learn about these bikes
In fact and for the 1st time I think I've just had an ATU fail on one of my CDI CX.I have spares but am investigaing as well speak.I have not seen anyone post this problem before in any other forum so it's another un-charted area to learn about.
I've just serviced the engine and put it back in but was having what I thought were carbs problems but now I think I've narrowed it down the the ATU unit(Automatic timing Unit) as it's impedences are out of the service limits.
This is a rare problem but one that with the age of the bikes may occur more.