There is a Gene song called ‘left-handed’; it may or may not shed some light on this. But I can’t remember the lyrics. I’ll have a listen later on.You are right the David Bret 'book' is tragic but I do agree with him about that. Perhaps it is a generational thing, but I've known and had gay friends use the slang 'leftie' as a a metaphor for being gay. It did come from the idea that being left-handed is somehow naturally wrong, hence someone who is gay is a leftie. Please don't shoot the messenger but I've heard that slang many times and actually assumed most people were aware of it TBH.
So yeah, a Southpaw in boxing terms is also a leftie. We must remember that this album was recorded post-breakup of Morrissey's first 'proper' relationship. By all accounts Jake was at least a amateur boxer and ignited an interest in the sport for Morrissey. So i always took the album title as something of nod to that relationship. In The Operation he is even more explicit,
'You fight with your right hand' (the boxing part) 'and caress with your left hand' (the homosexual/leftie part.) \
As for Southpaw, wow what a stunning song, I always assumed that 'the girl of your dreams' might hark back to Morrissey's teenage obsession Ann-Marie McVeigh, and the idea of what 'normal' (coda for straight) life might have been like had a relationship like that have worked out for him.
Anyhoo, all just specs-u-lation.
And being a leftie is also slang for being a total wishy washy c***...oh no, wait-that’s just in politics.