According to the American Tinnitus Association, tinnitus is
...the perception of sound in the ears or head where no external source is present...The word comes from Latin and means "to tinkle or to ring like a bell."
In almost all cases, tinnitus is a subjective noise, meaning that only the person who has tinnitus can hear it. Someone with tinnitus often describes it as "ringing in the ears," but people report hearing all kinds of sounds: crickets, whooshing, pulsing, ocean waves, buzzing, even music.
I heard about this problem a while ago, and assumed it was pronounced "ti-NIGH-tus" but when I saw a television report about it, they pronounced it like "TI-nitus" (the first part being pronounced like "tin").
So what's the right pronunciation? No one knows, not even the American Tinnitus Association: "Both pronunciations are correct; the American Tinnitus Association uses ti-NIGHT-us."
I thought finding an audio file at a website would settle the dispute, but there are different approaches to this minor yet confusing word: Mirriam-Webster dictionary pronounces it "TIN-itus" but yourdictionary.com pronounces it "ti-NIGH-tus".
I can see a bunch of nerdy linguistics discussing this word in conferences and in academic journals. I'm not nerdy enough to seek those out or bring up the issue in meetings. So you be the judge.