I did a couple of searches without hitting anything so here goes,
I’m reading Life on the Mississippi, by** Mark Twain**, originally published in 1883 and I came across an interesting use of fag on the last page of chapter 32. They’re describing a town that was wiped out by a change in the river, it washed it away leaving (paraphasing) neither hide nor hair, stick or shingle except the fag end of a shanty and a chimney you can see sticking up out of the water.
Now they don’t explain what the fag end of a shanty is, but if it’s synonymous with back end, tail end, bottum end, etc., the leap to homosexual, or cigarette isn’t too far.
Tried to post a link, but can’t from this location.