How do stock volatility halts work?

Well, I googled your question and found this article. It’s helpful, but doesn’t provide a specific formula for “acceptable trading price range (ATPR)”

https://centerpointsecurities.com/stock-market-halts/

There must be an official Nasdaq rule book for this but I haven’t found it yet.

The trading halt was a "LULD pause", as can be seen in this table obtained from the NYSE's historical trade halts webpage:

The Limit Up/Limit Down (LULD) mechanism is defined in the SEC-approved NMS Plan to Address Extraordinary Market Volatility, which regulates trading halts in Regulation NMS securities. The associated FINRA rule is 6190. Compliance with Regulation NMS Plan to Address Extraordinary Market Volatility.

For more accessible information about LULD, refer to:

• Nasdaq: Limit Up-Limit Down FAQ
• FINRA: Regulation NMS Plan to Address Extraordinary Market Volatility Plan FAQ

What determines how long a stock volatility halt will last?

To simplify, the "maximum" pause time is 10 minutes, but the primary listing exchange could choose to pause for longer than this. If the primary listing venue does not resume trading after 10 minutes, other trading venues are permitted to start trading in the stock. Note that there are exceptions which are all detailed in the NMS Plan to Address Extraordinary Market Volatility PDF.

Also, what exactly is the trigger for a stock's trading to be halted due to volatility?

To simplify, there are price bands that are determined based on the stock's price in the previous 5 minutes. When the stock price breaches these price bands, trading in the stock is halted market-wide. All the details are in the NMS Plan to Address Extraordinary Market Volatility PDF.

As for the cause of GameStop's 13-14 minute pause on 2021-02-24, the stock exchange probably decided, at its own discretion, to extend the pause right to the end of the trading day (16:00) because activity related to NYSE's closing auction begins at 15:50, or perhaps because there is significant order imbalance in the stock, which makes reopening difficult. These are just guesses on my part.