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I distinctly remember the first time I looked at a overly long and complicated model class and thought: "OMG, this is a state machine!" - a shortish refactor later and it was much simpler to read and debug.

However, now I'm at a loss on how to teach the junior programmers at my company how to recognize which patterns scream "turn me into a state machine!" Several booleans triggering certain code paths in several methods is a pretty sure sign. Are there more?

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The word "protocol" is a big red flag that you should be using a state machine.

The words "event loop" probably mean you need a state machine.

If "time" is an input variable, you probably have a state machine.

Your second and third points are why I love having state machines in the games I develop.

I've also found the presence of a mode variable a good indicator that a FSM should at least be considered.

If you have a "status" field in your object, chances are you can represent it as a state machine

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