my fuel level light has been on all the time for a few months--today I removed the fuel pump/level sender from the tank--four wires: brown, green, yellow white (in order)--I'm trying to figure out which is the fuel sender wire--am I correct in assuming brown is ground?--

couple more questions:
--is it okay to turn key to on(not to start position) without the tank/fuel pump/sender unit connected? I want to see if level light on dashboard is on or off when sender is disconnected
--in the wiring schematics there is a damping unit--where is it located on the bike?
--is it possible for this damping unit to fail? if it does, how does this failure present itself?

As you can see, I'm quite new at this, so please forgive my ignorance--
thanks for any help in solving this puzzle
Tony