What do you mean by "switch the unit on". Do you mean turn the S1 to the run position? Do you mean star the set up, and let it run? It would help you understand how the set pumps fuel, if you dug into the TM's. I am not at my computer, so can't post excerpts from the TM's, but the long and short of it is this. When the S1 is in the run position, (or aux fuel position) power is sent to the day tank float. The float is what tells the electric fuel pumps to run. If the level in the day tank is above the replenish level, the only way to get the pumps to run is with battle short. Knock on the day tank. Is it empty? Or full? Take a look at the -12 TM, and see how big the gen set fuel tank is. 10 gal fuel is not a lot. Was the tank compleatly empty when you put the fuel in? The last little bit of the tank can not be pumped. So that takes some away from your 10 gal.
What at I would do is put another 10 gal in, and then turn on the battle short switch. Let that baby run a while. Then you need to bleed the system. There is in all probability air in the system. After you have done that, reset your idiot light, "low fuel", and see if it goes out.