None of the first generation outdoors sinks drain into the grey tanks some have made various mods to address the situation. Some of the current newer units are now draining directly to the CG sewer via the RV sewer connection. They still do not drain into a grey tank but if you are on a site with a sewer this is a viable solution.
The issue is very basic the sink drain is lower than the grey tank. Water does not flow uphill. You can devise your own mod or use a 5 gallon bucket beneath the drain.
At this point the outdoor sink drain is a well known issue. I imagine 75% of them do not have drains . While the newer units are starting to have a provision for connecting directly to the sewer.
