Hello, bike not running off of choke is an indication that the pilot circuit in the carbs is plugged.. the choke is a enriching circuit hence why it runs only with the choke on. When turned off the bike starves for fuel and dies. My guess is the bike has sat for longer than 4 months and the pilot jets are plugged from varnish... they will need to be removed and properly cleaned.
I am not particularly familiar with any "91 Bandit 400,"but I can figure out something that simple, sight unseen!
Does the bike have ignition points and an ignition coil, or do you know? Secondly, does the headlight automatically come on when you crank it? With correct answers, we can get to the bottom of this issue quickly!
you don't need a firing order...left coil runs 1 and 4...right coil runs 2 and 3...it's called a wasted spark system...each coil fires 2 cylinders together but only one will be on it's combustion stroke at the time.