Addendum: Suspecting that my main account was ::ahem:: "too large" to /ghide as described, I made a third account with two new characters; inviting it as global friend and then using /ghide on one of the new characters.
Yes, /ghide did, indeed, globally hide both characters on the account with a single command, but failed when the account attempting to be hidden is larger than some unknown limit.
Thanks to all for your help.