Forer effect is more about general statements that can apply to anyone. What you're thinking of is confirmation bias - where we remember the hits and forget the misses.
Humans are very good at spotting patterns - but our accuracy is limited and so we will often overestimate or underestimate occurrences - we naturally see patterns, often when there is none.
As you rightly point out, it's very difficult to test in a real world setting - mainly because there is no practical way to ensure that you've noted each and every occurrence that should be included.
You can set up tests for it, but obviously those won't perfectly mirror the way these things happen in real life.
Interestingly, the world of online poker actually allows one to test this in real time. Many poker sites allow one to save all the hands played to their harddrive. Software can then run statistical tests on it. As one might imagine, poker is fertile ground for pattern spotting where people believe they see a certain pattern (ie: too many As coming out) - then when they go over the stats they will often see that their estimate was way off.