Is there any evidence that these mysterious 'whales' really control the bitcoin market, or is this a myth generated as people try to understand why bitcoin prices go up and down?
It is mostly a myth. Whales are called whales for some reasons.
They don't day trade like many others. Not sure how many whales are out there but I'm sure that they are pretty chill about their money when they look at the market. They are mostly longterm holders