Well seeing the moon controls entire oceans surely it's not impossible to imagine that it could possibly have some subtle effects on a human brain that is over 70% water
It's not impossible to imagine, no, but it should be provable. The position of the moon at the time of your birth is supposed to change your personality (moon signs that go alongside sun signs in astrology), yet nobody has been able to prove it does. If there are quantifiable changes in humans (more violent, more prone to cry, more excitable, more angry etc) then multiple studies should be able to show that.
Everything I have seen says it is a myth, with studies finding no correlation or, if they did find something worth noting, they were unable to replicate the results in further administrations of the study. Replication of results is important for proving a theory.
Studies have failed to find a correlation between the Moon and mental health. An analysis of ‘lunar-lunacy’ research published in 1985 concluded that there was no connection between the Moon and incidents such as crime, suicides and mental hospital admissions. A recent study in 2019, analysing the data of 17,966 individuals treated at various psychiatric wards over a period of 10 years (substantial sample size, longitudinal study) also found "no evidence that our celestial neighbour influences our mental well-being."
Many a study has been done to try to prove a link between the full moon and abnormal human behaviour, but the results have been murky at best. In fact, when a trio of researchers looked into more than 100 of these studies, they found none that could conclusively establish a connection between the full moon and human behaviour.
What they found instead was a subpar body of research that was conducted poorly or did not properly account for variables. For example, one study they analyzed showed car accidents are more likely to occur on the night of a full moon. But the data used for the study was collected on full moon nights that occurred on the weekend, when a higher incidence of car accidents occurs no matter the stage of the moon.
Also, the pull of the moon only creates tides in open bodies of water, like oceans and lakes (but only to a very small, almost unmeasurable extent in even our largest lakes). Closed bodies of water, like the water in our bodies, are not affected by this gravitational force.
Furthermore, while we are made up of a lot of water, the amount is actually miniscule compared to the oceans
Illusory correlations exist because we tend to remember events better than non-events. If something unusual happens during a full moon, for example, we take notice and even tell others about it. When nothing of note happens during a full moon, there's nothing to remember or tell others about, so this non-event fades from memory.
It's also possible that many moons ago, the full moon did, indeed, affect human behavior and that's why this idea still persists today. Some researchers believe the moon did lead to abnormal human behavior in the days before electricity allowed for indoor lighting and streetlights. In the days when many humans lived outdoors and slept under the light of the moon, the bright full moon could have made sleep more difficult, making people act different than normal or even exacerbating mental illnesses.