A fixed grin or forced smile; someone who is always grinning or grimacing, often insincerely.
Likely from 'grin' combined with 'agog' (wide open, eager), or possibly from dialectal or obsolete English sources. The term suggests both the fixed nature of the grin and something excessive or overwhelming about it.
The word 'grinagog' is so specific and odd that it feels like it should be a character type in Shakespeare—that person at court who smiles too much and makes everyone uncomfortable because you can't tell what they're really thinking.
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