Many of the same overall trends and features exist in gold ETFs as in the overall stockmarket. For example AAAU shows similarity to SPY. As seen here, why would an investment in a gold ETF follow the same trends as the overall stockmarket?
Why wouldn't they?
Companies that mine and produce gold products have shareholders, executive leadership, workers, labor challenges, HR departments, etc... just like every other company in the S&P 500.
They also have customers that may slow or cancel orders due to economic uncertainty, just like every other company on the S&P 500.
Looking at the correlation table for the past 6 months returns from ETF Screen shows a correlation of 0.18, similar to GLD at 0.16. That's pretty close to non correlated in my book.
What you may be referring to is what happened during the recent meltdown, it may have felt pretty correlated, but usually during a crisis, all correlation go to 1 (as it did during the 2008 one).