I noticed that when I shift into 1st the neutral light does not go out..lift on the shifter again and it goes out.
Sounds like your shifter ratchet is not letting it go far enough to get all the way into first.
Take the outer cover off again, put the shifter pedal back on and lift the pedal up into first. Note which way the linkage is working the ratchet and figure out which way your going to have to move the ratchet to make it go further than it is now (or grabs the tooth of the ratchet sooner so it will go a bit further).
There is only about 1/4 of adjustment so a very little will be the difference of shifting or not. The manual says that if you can't get enough adjustment out of it you can slot the holes out a bit more. I haven't found one that needed that yet.
Kind of a pain in the ass but by the time you get it adjusted correctly you'll have a complete understanding of how it all works and realize just how simple it all is.
On the good side, once you get it dialed in is will pretty well stay like that just getting better with age.
CJ