The engine and APU generator OFF BUS lights illuminate when the respective generator is running and of the correct quality.
This mean the eng bus off light only with lit up in the situation when engine gen WORKING. This is from http://www.b737.org.uk/electrics.htm.And your picture describe is right too，the light lit up because the Gen not connect to the BUS，but it not mean THE GEN NOT WORKING！！！！ >:(