Took my car to the dealership today. Demanded that I be present in the car when the tech takes it for a test drive. To my surprise I ended up driving the technician and repeatedly demonstrating the issue to him. He acknowledged the existence of the noise but wasn't sure what the issue was so he got the foreman involved.
I asked this technician about the high pitch chirping and he is fairly sure it is the Direct Injection system.
After a few calls to Gulf States Toyota (I think this is a regional distributor) and California, they still weren't sure what the noise was. Gulf States said they wanted the Foreman to bring the car over to listen to it. After the foreman and I went for another drive to get synced up on issue and noise in question, I hesitantly agreed to let him bring it over there. Overall I think they will put 80+ miles on the car before I get it back
Just got an update, they had another FR-S to compare it to. In the other vehicle they got the same noise to occur, but it happened much more quietly. They said you really had to listen for the noise. In my car it was much more pronounced. Ultimately they are convinced it was something in my transmission, heard something along the lines of "harmonic balancer". They recorded video, documented the issue and sent it to engineers in California. They deemed the car safe to drive and said there isn't an impact on reliability so I'm getting the car back tomorrow. They aren't sure but they are researching the issue.
I'll continue to touch base with them and get updates. They told me if anything had to be done it'll be covered under warranty.
For anyone who wants to hear this flutter engine noise I'm hearing you can do it two ways. Get the car warmed up first. Roll up your windows. Turn off the radio. Now either
1) get the car up to around 50mph in 5th or 6th gear. When its safe, put it in neutral and brake all the way to 0 with regular pressure like you are doing a normal stop. For me, right around 20mph you'll see the RPM dip and the engine make the flutter/sputter noise.
2) Get the car up to speed, around 45mph. When its safe, put it in neutral and let the car coast and slow down on its own. The Foreman was able to repeatedly hear the sound when it passed 36-38mph.