Ok, I completely disagree with the 'if you don't look like it then don't claim it'. That's crap. You can't help what you look like. Using this logic, a light skinned African American should never acknowledge that they are black?? Yeah, doesn't sit very well.
I am Native, so I will just tell you how it's worked for me. I am 1/4, and have been asked about it at every interview. Be prepared to talk about your background. I don't think they are looking for epiphanies, just how it has influenced your life (mostly it's influenced mine by my grandparents/parents not having opportunities). Are you registered with the tribe, or at least have your family name on the roles? I know at least a few schools have checked me out, as they wanted exact listings (what SPECIFIC clan of tribe, where they can locate my family name, what location it's registered under, exact spelling of family name, etc). If you can match these criteria, you're fine. If not, it may be in your best interest to not check the box. If you feel like you have enough life experience to back up applying as such, make sure you check the other boxes that correspond to your background. If you don't look like the typical Chief Running Water (and let me tell you, such an incredibly small percentage do!! I live in the town with my tribe's reservation, and most of the people on the rez are even straying from the stereotyped image of a Native American), they're not going to be surprised when they see that some Scottish was also mixed in. If you have any specific questions or concerns, PM me! This will probably get moved pretty fast to a different spot...