Stock prices are determined at the marketplace. However, just like you stated, there is not a clean connection that tells us exactly how a stock price will go up or down. However, three are three main category of forces that impacts stock prices. Those are fundamental factors, technical factors, and market sentiment.
fundamental factors, at a very basic level in an efficient market stock prices would be moved by ratios or data that comes from a company's balance sheets. Two of those are earnings per share and P/E ratio.
Earnings-per-share is company's profit divided by the outstanding shares of its common stock. The P/E ratio is current share price relative to its per-share earnings. representing an anticipated future earnings stream. Many use cash-flow-based measures to determine whether they buy or not. They also use it to see the perceived risk of the stock.
technical factors are mix of external conditions that alter the supply of and demand for a company's stock. For example, the growth in gdp.
But here is a list of other economics indicators that can have an technical impact on whether someone buys or not:
Production output growth of industry/market
Incidental transactions: purchase or sale of a stock motivated by something other than the value of the stock.
Demographics of investors. Are they middle aged or older investors.
Trends in the market.
News: what is happening in the world can impact a company finances. Political situations or negotiations between countries can and does have an affect too.
market sentiment, which is referring to how market participants believe or feel, individually and collectively. This is the most frustrating category. Market sentiment is often biased.
The question asked was “is there some non-obvious benefit to abruptly "betting" one direction and then the other, or is some sort of mechanical market force at work”.?
To answer that I would say, "possibly"; because of market sentiment of a particular demography of market participants. They may get the pleasure of feeling good about betting in a particular way when to others it is non-obvious to do that.