How would I test it experimentally if they can't vocally express this awareness?

Just like you can run implicit racism tests I think you likely also can run texts where you let participants read various statements and measure their reactions.

fixed-mindset - When individuals are praised for their attributes, they are more likely to engage in behaviors intended to display or protect those attributes. growth-mindset - When individuals are praised for their effort, they are more likely to engage in behaviors intended to improve their attributes.

I think that points to part of the experiments but it doesn't explain the whole concept.