Spot gold has little to do with the US stock market.
Generally speaking, it has something to do with the dollar, because spot gold itself is denominated in dollars, but these situations are not inevitable. It does not mean that gold will fall when the dollar rises. I've been through this myself. Of course, the same is true of US stocks. The rise of US stocks will affect a person's investment from gold to the stock market, so gold will generally fall, and some people who fall in US stocks will also invest money in gold to avoid risks and let gold rise, but these are not inevitable and need specific analysis.