Actually they would associate the stick with a number of things, including but not limited to the stupid thought process. They would be quite likely to associate the stick with their encounter with Eliezer, and to their (failed) attempt to converse with and/or follow his thought processes. Mind: They associate the stick with all aspects of the attempt, not only with the failure.
It might work in a Master/Apprentice scenario where the stick-hitting-victim is bindingly pre-committed to a year of solitude with Stick-Happy!Eliezer in order to learn from him the art of Cognitive Kung Fu. This is the only scenario I can immediately visualize in which the stick-hitting victim would not immediately decide that Stick-Happy!Eliezer is a person they can get away with avoiding, and possibly with reporting to the police for assault.
EDIT01: This is assuming that the experiential sample size is 1.
Easily reduced, in theory; educate them about the false dichotomy and other basic fallacies -early-, and have it cost them marks when said basic fallacies punctuate their thinking, the same as any other error.
Of course, it’s not so easy to get that implemented in the broader system, in a world where people refuse to be taught how to think. But while we’re talking about the “ideal” education...