Sorry to correct you, Fionn, but you are confusing two uses of 'single/double' here. A tune can be played single(ABAB) or played double (AABB),which is a matter of convention and as you say, is not always clear when a tune is written out.
The other use of single/double refers to the rhythmic complexity of a tune. All jigs are in 6/8 time, but you get more notes to the bar in double jigs! Most 'ordinary' jigs are double jigs; an example of a single jig is 'Off she goes' (Humpty Dumpty). BTW Kerry slides are a particular subdivision of single jigs, rhythmically distinct.
Similarly, most 'ordinary reels' are double reels. 'The Rakes of Mallow' is a single reel, as are the Kerry polkas.
There is of course another usage of single/double, and after a few of those it's very hard to remember how many times you've played anything! :o)
Hope this helps
--Noreen