Assuming the battery is just old and bad, which definitely sounds likely to me.
Check the battery with a voltmeter, the conventional wisdom is that it should be giving out over 12 volts with the bike off, shouldn't drop under 10 volts when you start it and should show over 14 volts when the bike is running to indicate the bike is charging it.
I'm having a bit of trouble deciphering what you actually connected where, though. Punctuation is a good thing...
There is a known issue with the keyswitch not being able to handle all the electricity flowing through it and then failing eventually, bad design choices by Triumph, which might be something to look at if there's an actual fault.