So to answer your question on how fast it needs to pump... As far as pumping action, if the pump is not already primed you will initially hear a "fast clicking" sound until its primed, then a slow click every now and then to maintain 6-8 psi pressure flow until the AUX tank float switch turns off when day tank fills properly.
Also, your probably already aware but just to cover all the bases for anyone else that reads this... your 55 gallon drum itself must be vented when you are drawing fuel from it. Otherwise, if everything is sealed up air tight on a 55 gal drum bung/vent it will draw fuel until it creates a vacuum and causes pump to stall or possibly barrel to deform
. But as Scoobyshep mentions above, all the fuel transport fittings & hose must be air tight no leaks.
With you having verified your solenoid valve as opening completely, it points to your pump. If you have cleaned the bottom screen filter then its possible your Aux pump internals might be gunked up due to non-use over time. I would remove the pump and try soaking/flushing in a cleaner, acetone cuts the varnish/gunk quite well. If it looks really bad these pumps can be completely dissembled and "usually" restored back to full operation unless they are electronically toast internally.
As an alternative, you could swap in your redundant 2nd main pump (assuming it still has one) to the Aux pump position with solenoid connected to it and test that it functions properly with a different pump. BTW, its perfectly fine to run the generator off just one main pump. Having the 2 pumps ganged in series are for redundancy purposes for remote military fail-safe operation. Civilian use owners often remove the 2nd main pump to hold as a spare for whenever it might be needed as a swap in replacement pump.
Also, if you were to replace any of the pumps...be especially careful when replacing the Facet pumps with other models on the market. If you choose to maintain & run the main "dual pump setup", you always have to make sure those 2 pumps are matched up to the flow-through type design pump. The original pumps were stamped with a P/N on their mounting flange. IIRC, the pumps were stamped "480517E" on mounting flange. There may be later pump models that superseded that particular one that are equivalent that are of the flow-through design for dead pump redundancy operation. However, if running just one main Facet pump, the dead pump flow through feature, is NOT required...that is as long as the chosen pump can produce the 6-8 PSI pump pressure and it will NEVER be paired up in the future with 2 pumps run in series.
