What technical tools can I use to help predict whether the S&P 500 will rise or fall tomorrow? (Assuming no major events occur)
The S&P 500 goes up most of the time. So just assume it always goes up. You will be right most of the time. This is the basis of most investment advice: diversify to match the market rather than try to beat the market.
If there were a technical tool that anyone could use that could consistently determine if the S&P were going to go up or down tomorrow, it would stop working almost immediately. Why? Because the best way to take advantage of such a tool is to sell it to someone like the Wall Street Journal or Bloomberg. Then they'd publish it. Anyone could get the results. And if you know the S&P is going to go up tomorrow, you can buy today. What happens when you buy today? The stocks go up today rather than tomorrow. But then the tool is wrong about tomorrow.
It is possible through analysis to find gaps in the current stock market consensus. But this is an ever-moving target. As soon as the analysis becomes common, it becomes the market consensus, and you have to change to a new analysis. This makes for a bad answer here, as what we might tell you (if we knew) will be wrong next month even if it is right today.
The best that we could do is point you to Google results, like 5 Tools for Stock Traders. That basically says to buy a good charting tool.
The truth is that anyone who has an accurate technical analysis tool is not posting here. That person is busy trading and making money while dreading the moment when the rest of the market catches up.
My high school economics teacher mentioned that when she worked on Wall Street, she and her coworker would make daily bets on market performance. Her coworker would use a bunch of market data, and she decided to look at the weather (nice day = market up; gloomy day = market down).
She said she won more often, but then again, she's not on Wall Street anymore.
The Yield curve.
If it inverts, the recession is likely (or certain depending on how much you trust the model explaining inverted yield curve vs recession); and thus equity markets will (eventually) fall and the major indices (including S&P) will tend to go down for a while.
Otherwise, on average, the markets are more likely to go up than down, as per Brythan's answer.