It seems that setting a goal based on the site search URL pattern doesn't work if you've enable site search tracking. I see that the typical pageview has been replaced by the site search icon in visitor logs, but it seems to me that the URL should still trigger the goal.
(I'm not sure if anyone in the forum issue from years ago created an issue.)
Having this out-of-the-box would be really helpful. We use search patterns for quicklinks quite often and right now, we can't track whether they are used or not or to what extend.