It puzzles the life out of me does all this. The differences in the bikes, batteries, leads, starters etc etc.
My bike, a 2011 TC with just short of 70k up of which i've added 50k in about 4 years and in that time it's
never failed to start no matter the weather and in temperatures ranging from -10 to + 45C,
When i bought the bike i put a Motobatt on it that had seen service on my previous bike so it's now done well
over 50k and is over 4 years old; still going strong and fires the GS up even after being stood for a couple of weeks.
I have never touched the starter, never needed to, not got any special leads, connectors or anything, just the standard set up.
The only dodge the bike has when starting is (it's always done this) the engine turns then stops momentarily only to turn again and fire up;
a bit disconcerting at times but as i said, it's never failed. When my Motobatt fails (which it no doubt will) there will be another going on.
In my view, if everything is right, and working as it should, there is no need of special leads, connectors or anything as hundreds of thousands
of these bikes get along very well without them.
As i said, it's a puzzle
To the OP, the current drain isn't good and will take the battery down. Something you said earlier about the current drain starting at a certain level
only to drop back to a lower level brought to mind the possibility of a leaking capacitor somewhere on a circuit board. Just a thought.