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So, it just occurred to me that for all of the "reach" firms I got a callback from, at the end of the interview I said. "I really want to work for ___firm name__." Or, sometimes just, "I really want to work for you." This is said in the context of towards the end of the interview awkward "do you have more questions about the firm?" after you have already asked many questions and the interview is just about to conclude.

Didn't your OCS tell you? That's the secret callback password!

"It was really nice meeting you I REALLY WANT TO WORK FOR YOU and I hope you have a great day."

Haha this didn't work for me the numerous times I tried. It also led to what was probably my most awkward exchange at OCI.

I did this exactly once and got a callback. I consider this conclusive proof that OP's tip is valid.