Hi Bob good to see another CL70 getting back on the road! Great bikes and everyone sees how useful they are and realizes they are valuable bikes.
The ground is definitely your biggest problem and needs to be corrected before any further troubleshooting. The ground from the battery typically goes straight into the wiring harness plug. This negative signal is grounded to the frame at the tail light and also the rectifier so it was not grounded to the frame at the battery compartment from Honda. They wanted to make sure the battery ground went to the rectifier first which requires a very strong signal -well as strong as a 6V battery can produce.
The rectifier controls all the juice that the bike gets so you need to make sure that you find that wire that goes to the rectifier and connect it to the ground side of the battery. Or you can grab your own wire and find which terminal is the ground on the rectifier and connect that to the battery outside of the original harness. It's not a bad idea to connect the battery ground to the chassis but it's not necessary.
When I was young I noticed that when I cleaned up some of the connectors and soldered a couple connections that the electronics worked much better. So I just soldered everything together at that point... turn signals, horn, everything. People might say that's not good cause what if you have to replace something? Well I'll cut the wire and solder on a new one! But I've NEVER had to replace anything on the bike besides the battery (which I use connectors for the leads). And the bike runs awesome, starts easy and the lights are twice as bright and horn twice as loud as when I got the bike way back then.
Let us know how it goes. I'm sure the electrical signal is being degraded between the horn, lights and switch. But at least if you take care of the ground the rectifier can do it's job and the battery will charge and the engine should run better.