Does the taillight dim when you press the brake?  What happens to the voltage right at the battery?

Can you have someone closely observe the filaments in the bulb?  It could be both are lighting up with tail and brake activated but you can't see it get brighter due to the voltage drop. 

Would a bad earth cause the tail light to attempt to earth through the other filament. I'm not sure but have seen faulty earth's causing all sorts of backflow on bikes. How about connecting your new charger to the battery while it's still connected to the bike so you know you have a full 6+ volts constantly, then activate indicators, brake light etc, anything battery related--& horn. Could try them all together at once as just might have a situation where that is required in reality. Are 6 volt batteries available on higher grunt capacity. Not sure what I mean but in my car it would be higher CCA cold cranking amps I think I mean?.

Good morning guys, so I connected my volt meter to the battery and tested with key in second position with brake pulled, voltage drops, then in third position it drops even more so I gave a close look and yes indeed the second filament is lighting, albeit ever so slightly, so taillight is fixed, thanks to you guys!  As for the horn, when I hit the button the volts drop drastically but still no sound from horn.  I need to find one that I know I have, perhaps it's gone on the walkabout with the other charger

Congratulations Tony!

It sure sounds like that battery is pretty weak. 

Thank you Mark, all your help is much appreciated!

You're welcome Tony!  A few years ago you helped me out by sending me a bunch of photos of the wire harness routing I needed.  Happy I could return the favor and help you out a little.