All I could think through the whole day was that we missed my brother’s football game because of me, and I really hoped my sister thought to tape it.
—The Perks of Being a Wallflower
It looks like it meant "remembered to". But is this a usual usage with the word? Can someone point me out a legit source for this definition?
It’s a very common usage.
To think to do something – Have sufficient foresight or awareness to do something.
I hadn’t thought to warn Rachel about him.
Now your sentence –
I really hoped my sister thought to tape it.
This means that I hoped my sister had a sufficient insight before/during the match to record his brother’s football match.