Mine always took two tries. It always started though.
It's unrelated to your issue, but your neutral light issue is a symptom of a failing neutral switch. The bike needs to "see" the green light to realize it is in neutral for the start sequence. If your green light disappears completely you will only be able to start with the clutch in, like it's in gear. The clutch switch is a little unreliable too so you may find yourself unable to start the bike some day. Even that's not a huge deal, because you can jump the wires to the clutch switch (or replace it). You can also pull the starter relay and jump hole 2 to hole 6.