Not entirely sure of problem from your description...what is 'drain spigot' you refer to?
Pump should run to address flow needed--will pump more if more than one tap is open.
What happens if you open sink and lav at same time? How well does the toilet flush?
My first thought is you have some blockage--have you checked the strainer on the pump? But if it was the strainer, it would never pump good.
More details, if possible, will try to give some more ideas.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired