i had the same issue within a week of getting my teg lol..its an easy fix...just open your trunk and on the left side, like right above the left rear wheel, under the trunk liner is the drainage pipe from your sunroof. couldve just gotten disconnected and now dumping all water into the spare tire section.
not trying to be mean, but when it was rainy season a couple weeks ago... many threads were brought up, but many OLD threads have these problems with solutions
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BUT it could be your tail light gasket, sunroof/moonroof drain tubes...
Yep, really common problem with Integra's. I had the same issue DVS, I changed my taillight gaskets even though the old gaskets looked fine, and no more water in the hatch since.