UPDATE: Oh man, I think I'm dealing with two problems at the same time, but I may be getting to the bottom of it. I think "Patrick L" hit the nail on the head with his response above about having two issues at the same time
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I've apparently got a bad ground by the passenger side tail/stop light fixture. A wire lead with alligator clips between the fixture housing and a bolt on the luggage rack allows the brake lights to work properly (assume that adds a proper working ground), BUT the brake lights still only work if the headlights or cowl lights are turned on.
So, I then went back and again bypassed the "bail" by adding a direct lead between the starter switch and the brake light switch.
With the "bail" bypassed, AND with the extra ground on the light fixture, both brake lights work properly when the brake pedal is depressed.
So I think I need to fix two things. The bad ground at the rear passenger light fixture, AND I probably need to investigate/take apart the "bail" to see if something in there is loose or crossed?
Does this sound like a plan? As a newbie, I am nervous of messing with that bail, so I'll have to do some research on threads here first before I attempt to take that off/apart.
How would I go about fixing the fixture ground problem? (without adding a permanent/additional ground wire if possible). Is it just a matter of seeing if the bulb housings are rusty, or ??
Thanks so much for the help!