The engine shuts off immediately after I shut off the ignition. listened to it a few more times and the squeak/squawk sound seems to be under the intake manifold. It sounds a little like when you let a little air leak out of a balloon.

Any chance there is a vacuum hose under the manifold that is leaking?

What gets de-pressurized when I shut off the engine? Sure sounds like something is de-pressurizing (hiss after the squeak).