Absolutely, Eeyore is a much richer character than Gemini Pro! But I do tend to hear it in some combination of (my internal version of) Eeyore’s voice and Stephen Moore’s Marvin.
(Don’t worry, I’ve read those books a hundred times. And yes, stick with the books.)
You need to reread Winnie-the-Pooh <https://www.gutenberg.org/cache/epub/67098/pg67098-images.ht...> and The House at Pooh Corner <https://www.gutenberg.org/cache/epub/73011/pg73011-images.ht...>. Eeyore is gloomy, yes, but he has a biting wit and gloriously sarcastic personality.
If you want just one section to look at, observe Eeyore as he floats upside-down in a river in Chapter VI of The House at Pooh Corner: https://www.gutenberg.org/cache/epub/73011/pg73011-images.ht...
(I have no idea what film adaptations may have made of Eeyore, but I bet they ruined him.)