Why can gold fail to act like a clean safe haven during a geopolitical shock, while oil and the dollar strengthen at the same time?

I’m trying to understand the economic logic behind a market pattern that seems counterintuitive at first.

In the current Middle East conflict, my first instinct was that gold should behave like the clearest safe haven. But the actual market reaction has looked more complicated. Gold can spike at first, then lose momentum or even pull back, while oil rises on supply fears and the U.S. dollar also strengthens. At the same time, people start talking about higher inflation risk and fewer rate cuts.

From an economics perspective, what is the cleanest way to think about this?

Is the basic mechanism something like this: geopolitical risk raises demand for safe assets, but if the same event also raises oil prices and inflation expectations, then markets may price a higher-for-longer rate path, which supports the dollar and reduces the appeal of a non-yielding asset like gold?

I’m mainly trying to understand the transmission mechanism here, not to ask for trading advice. In other words, why can one geopolitical shock support gold in the very short run, but then still create conditions that work against a sustained rally?