Your words give lie to that - in order to "experience our perceptions" there has to be a 'me' in there. You know what I'm talking about - the guy in your head that you are aware of at all times.
Behavior is observed from the outside. But what about that 'feeling' you get inside your own head, that you are really there? The act of observing it means you are something else than the behavior.
Not really. In a programming language, for example, there is a feature called 'introspection' where the program can examine an object in memory as it runs and determine its type. It doesn't mean the program is self aware. I can think about how I experienced something - but it's just a neural computation 'about' another neural computation. No magic.
Behavior is observed from the outside. But what about that 'feeling' you get inside your own head, that you are really there? The act of observing it means you are something else than the behavior.