As versy said in your original post:
"prob#2-if you have a California bike, there's a carbon canister under the swing-arm.
And there should've been a 3/16" line running from the tanks vent to it.
Then another line will run from the canister to the carb.
The parts are shown in the canister (E33) section of the phish"
Here is the phish he is referring to:
https://suzukiofvannuys.com/Parts/Parts-Fiche/suzuki/motorcycles/1996/ls650p-...That tube SHOULD run to the evap canister, if there is one. If that is missing from your motorcycle, then .. it probably doesn't matter where it goes, as long as it doesn't drain on to something HOT, as it is the vent for the gas tank.
OR, you could cut it short and cap it off. (or just cap it off at the tank)
If you do that, you may need to have a VENTED gas cap that allows for air flow both ways.
I don't know if you could modify the current gas cap. Probably.