For me this would be a complex piece, nevertheless if trying to sort it out first I'd get hold of a MIDI version, for example at ...
http://midistudio.com/midi/JT_AZ.htm
... which I'd then download by highlighting the song name that appears there, doing a right click, selecting 'save link as', then choosing (say) 'desktop' as the download destination.
Next I'd run a MIDI sequencer (in my case Band In A Box) and import the song just downloaded. I can then see that its in the key of F (kicking off with a Bm7b5) and away we go from there!!
BIAB allows several things to aid getting one's head around a song like this (which to be honest I'd never heard before) in that it can be slowed right down to see how the thing progresses, the key can be changed to something other than F (in Eb, for example, it starts with an Am7b5 chord), we can look at the score, look at how the tune appears on a piano or guitar keyboard, follow the bass line through (which I usually find helps) and so on.
It took me about three minutes overall, from reading your post, to then get the tune found, downloaded and playing in BIAB with its key changed to an arbitrary Eb, so I reckon its a useful approach. Once the structure of the tune is nailed down then any sax bits one might want to add is really just a question of doodling along selecting notes from the bass line or whatever chord is being played at the time.
While doing the above I'd also troll around the net listening to various versions of the tune, both instrumental and vocal. Before long it would all start to sink in.
That's my take anyway!
Hope helps ...