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Is this where the character doesn't change to fit in better? Otherwise, it may be Wrong Genre Savvy - unless you're saying that the character is aware of the genre conventions but still refuses to obey them.
The idea I'm looking for is the character that is aware of the genre they are in, but refuse to take a part in it simply because it's not their thing. Like a character can witness a Crowd Song, but refuses to sing along, no matter how much he is prodded. Or maybe everyone is trying to get him to Clap His Hands If He Believes, but doesn't, even though clapping wouldn't really hurt him, and he may even believe that it would help, but still refuses since he'll feel silly doing it. Basically, there's a trope that is common and even expected in a universe for everyone to participate in, but one character refuses to participate, often for the only reason that the audience wouldn't do it.
I think this is what you're looking for:
https://tvtropes.org/pmwiki/pmwiki.php/Main/MetaGuy
If that's not quite it then it might be one of these pages. These aren't quite what you're looking for, but if Meta Guy isn't it (although I'm pretty sure it is!) then you might find a lead here:
https://tvtropes.org/pmwiki/pmwiki.php/Main/GreekChorus
https://tvtropes.org/pmwiki/pmwiki.php/Main/NotEvenBotheringWithAnExcuse
https://tvtropes.org/pmwiki/pmwiki.php/Main/AudienceSurrogate
https://tvtropes.org/pmwiki/pmwiki.php/Main/NarratorTropes
https://tvtropes.org/pmwiki/pmwiki.php/Main/TheSnarkKnight
https://tvtropes.org/pmwiki/pmwiki.php/Main/WhoWritesThisCrap
I had a feeling it might've been Meta Guy, but I couldn't really make sense of the description. After reading the laconic, I'd have to say it's exactly right.
Is there a trope for a "out of genre" character? What I mean is a character who refuses to participate in the tropes often associated with the genre that he is currently in. Like in a musical, the guy who refuses to sing and dance. In an action film, the guy that is physically inept and never Took a Level in Badass. In a happy, family friendly film, this is the Grumpy Bear on the cynical side of the sliding scale.