This photo should illustrate the solution pretty clearly. While I was at it, I replaced the plugs with Iridiums.
How do these old ones look?
My ST1100 was dead.
Turn the key and the clock goes dark and nothing lights up.
Posted my problems to the popular ST1100/1300 boards and did some digging.

Here's what I found:

 

That's the top of the Starter Relay Switch (page 17-5 of the service manual).

And that's the 30A fuse I discovered.

Another view of the relay.

I just inspected the relay over the weekend.  Obviously, I didn't look close enough.  The first view above really isn't possible until you disconnect and remove the relay from the bike, as it faces inward when installed.  I only found the problem when I decided to pull all fuses.
     
 
 

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