If the female protagonist has a small portrait or character art, I'll check her appearance and personality to see if she matches my preferred type; otherwise, I'll close it if I can.
I only feel a sense of identification with protagonists who share similar personalities, thoughts, and interests. For example, they might have the same hobbies (reading, shopping, working, etc.) or possess a strong sense of justice, not easily yielding, and having their own opinions.
I mostly feel involved when faced with game choices: I make decisions based on my own subjective perspective, rather than on the female protagonist's situation or personality. Even if the ending is unpleasant, I can accept it.