Mine kept coming on while the pump ran for extended periods of time. Is yours equiped with air ride or has it been replaced? If it is still equiped I mirror dandd response or it could be the same issue as mine. Leak in system causing the pump to run and overheat. Also, it may be a sensor in one of the levelers. The diagnostics should spell out which.
Only if the tire is rubbing the bag or strut guard. It sounds like a bad leveler valve not putting the right pressure in the left bag or you may simply have a bad strut or bag. A bad strut throws off the air ride and will make the light stay on because of excess pressure on the bag or "bounce" in the system. Best thing to do is have a Lincoln tech place it on the diagnostics machine.