How is circadian rhythm of gastric acid secretion regulated?
I'd suggest reading wiki first.

Autonomic nervous system, the one that regulates breathing rate, heart rate and other physiological processes as a function of circadian time, regulates secretion of gastric acid. Vagus nerve, part of parasympathetic nervous system (the one responsible for "rest and digest" part of behavior, opposite to sympathetic "fight or flight") stimulates secretion of gastric acid and regulated through circadian mechanism.

See also here, Circadian variation in gastric vagal afferent mechanosensitivity:


  Thus, gastric vagal mechanoreceptors display circadian rhythm, which may act to control food intake differentially at different times of the day.


This is another interesting review: Gut clock: implication of circadian rhythms in the gastrointestinal tract. It states that GI tract has its segments set their own circadian clocks, different for various segments. But all of them are operating and adjusted by main clock, regulated by, as I know, melatonin and orexin hormones.

Surprisingly, not much seems to be known about this connection. Pineal gland seems to be very important in this process, because it produces melatonin.