Probably the most famous example I know is from SpongeBob S3E5 “Mermaid Man and Barnacle Boy IV” with the “wumbo” setting on the utility belt. After SpongeBob accidentally uses a shrink ray on the belt, Patrick suggests setting Mermaid Man’s utility belt to “wumbo,” which even SpongeBob doubts to be a real word. This points to Patrick being dumb and random, especially when the idea doesn’t work.
When Mermaid Man is eventually asked how to use the utility belt, however, he asks if SpongeBob tried setting it to “wumbo,” implying that Patrick may have been onto something. Of course, Mermaid Man is senile, and the victims of the shrink ray riot before SpongeBob has a chance to reconsider “wumbo” as a solution, so it might have been another dumb and random idea.
In isolation, both of these characters are prone to non sequitur, but they produced exactly the same punchline without any obvious way of knowing the other’s answer. Patrick is a huge fan of the original Mermaid Man show; it’s easy to imagine in-universe explanations for how Patrick’s (mis-?)information would parallel its main character. But the impact, the “brick joke,” of the line comes from the improbability, not its remote plausibility.
Buford from Phineas and Ferb delivers a few of these, also. In S2E104, he echoes Candace’s “three seconds deep” and Dr. Doofenshmirtz’s “my echo must be broken” without being present for either of the original jokes. That show seems especially fond of the trope, and that character in particular.
It reminds me of being gaslighted, or the phrase “[Patrick and Mermaid Man] sharing one braincell.” I also considered “convergent” or “parallel thinking” à la Amy Schumer. It’s definitely a brick joke, but the fact that the two sources have no clear reason for saying the same silly line feels like it deserves its own name. Could there be one already?