Well, it's a function of detoxification versus a function of digestion.
When drinking the flush potion at 10pm you are setting up the expulsion of bile into the flush chyme sometime around the A.M, when detoxification is at its prime. The recommendation for this late night intake could also have been to "sleep" away the inherent nausea and discomfort. But I have found the potion to sit in the stomach all night and not be released from the stomach until morning, when the gallbladder actually pumps out bile.
Walking after taking the flush drink or drinking it sometime earlier in the day optimizes digestion, creates movement and circulation which optimizes the production of bile and the contraction of the gallbladder. More bile being released maximizes the expulsion of intrahepatic stones and biliary sludge. I have tried both, and both work.
Try both! Resting flushes and active flushes.