I thought I'd commented on this before, but:
For once, you've lost me! What's timeless about "fag" (ITC) and why does "bag" make more sense? To me - it makes sense, period!



I have to admit, I've had a drop or two myself
My visions kind of fuzzy and my legs aren't working well
If a copper stops me now, by breath would set his bag alight
So keep me off the road and let me stay all night

In context I would have to say 'bag' is the correct option.
The singer is admitting to signs of intoxication. If he were stopped (while driving) by a 'copper' (policeman) he might expect to hear those imortal words "Would you just blow into this bag sir?" as the early form of breath test involved inflating a plastic bag by blowing through a tube of crystals which change colour in the presence of alcohol. The bag ensured that a sufficient quantity of breath had passed through the tube to be a valid sample.