For a TPM role, you should expect a full loop of eight people. Typically you will be in one room for the duration and they will tag team you for most of the day. The interviewers do not have contact at all until the debrief which is likely to be the next day or even days in the future. So expect to be asked the same question over and over.
At least one and perhaps more will be technical interviewers. To be a TPM at Amazon the rulebook says you need to have experience in software development. While this requirement is enforced to greater or lesser extent for each role, a key precept of Amazon hires is they must be "fungible". Here's the logic: If your team blows up tomorrow, and you land as TPM of a DevOps team building a web service, can you make the transition?
So don't be surprised if you are actually asked to code something. Definitely have crisp answers for high level questions like "what languages are you comfortable with" and "are you comfortable designing a relational database schema". And if you don't code daily in your current role, if it comes up plainly say so - do not stumble around trying to bluff people and get on the bad side of your interviewer. The interview comments in the system last forever.
How should you prepare? Amazon does not value trick questions so do not expect lateral thinking puzzles or nonsense. Expect each of your interviewers will be assigned an Amazon Leadership Principle to target, beyond that they'll all be freestyling based on how they like things to go.
So knowing this going in, you can be successful for any approach if you prepare and rehearse in advance a brief anecdote to illustrate each Leadership Principle at http://amazon.jobs/principles. And the action of preparing the anecdotes will focus you on your history and proving you are a candidate that can deliver results.
Why is this critically important? Amazon believes past performance is the only reliable predictor of future performance. For core skills, Amazon never hires someone to "learn on the job". Thus coming into an Amazon loop with a mindset like you will win people over and get a job you've always wanted but never performed before - please don't waste your time and get disqualified. We are largely engineers and very left brain about evaluations.
