I received a notification that there was a like on this topic so I thought I would update my previous dillema. I was a good girl and hired a plumber to connect the outdoor sink to the house at a cleanout. It was about a 25' run, curved and piping went up to the cleanout about a foot. Plumber installed a really cool pump under the simk that when full will push the water through. There is a very quiet flushing sound when the water is at capacity. No one can really hear the flush unless you are pointing it out. Job with equipment/materials ran $850 but Hubby and I did the digging for the piping. The original quote including all labor was about $1600. We added a clean out in the yard in a valve box and then another one to replace the one we tapped into. The cleanout piping at the house is quite an eyesore, but we bought a fake rock to sit over it. Outdoor kitchen is finished and I haven't screwed up the drainage.
Q