In Florida, mestizos and people who look like Zimmerman are pejoratively referred to in the Latino community as "indios" (even by African-Latinos). Latinos that call themselves "white" around me are usually of full-blooded (or at least look so way more than Zimmerman) Spanish / French / Portuguese / European Jew / German, etc, ancestry. Reactionary white Cubans in Dade will tell someone like Zimmerman that he's not white in a New York minute. Having an indigenous mother and a white father doesn't cut it. And in Peru he wouldn't be white, either. The more dominant the fully white section of the population is, the more jealously they guard access to "whiteness".
Some of the variation in terms is due to the vast variety of racial classifications depending on whether the national origin in question is part of either the black/white, brown/white, or mix-of-all-three region. Peru is generally regarded as "indio", or part of the brown/white grouping, even though there are significant black, white and Asian populations as well as indigenous. There's plenty of racism, but unless they're Americanized, most mestizos that I speak to who are clearly mixed are usually trying to claim the meaningless "Hispanic" designation. I always see that "white Hispanic" designation on the FBI's Most Wanted List at the post office as well, with these guys with features that look like Geronimo.
Post-script:
I thought about what you said a bit and agree to some extent, once I thought about Zimmerman's background. Thinking about him being brought up in the US, I can see him viewing himself that way, based on his father and upbringing as a judge's kid. I have encountered some biracial children of a white parent and a non-black minority parent who identify as white if no one challenges or questions the self-designation, and if they're not raised around a significant population of the other race to foster identification with them. Sort of like black Dominicans self-identifying as white if they have even a trace of white ancestry.