I was wondering, if we measured the carbon isotopic ratio of methane on Mars and found that it was very negative (i.e. it contained more carbon-12 than carbon-13), would this provide definitive proof that life exists on Mars.
While a negative δ13C could reasonably be considered possible evidence of either current or past life and perhaps suggest good places to look, it would not be definitive proof.
All you know for sure is that some process is separating isotopes, probably some form of kinetic fractionation. Although this can be biological, there are also non-biological examples, such as water in clouds containing lighter oxygen isotopes because they evaporate more easily from seawater.
Interestingly, a higher ratio would not conclusively disprove biological origin either. Even on Earth, different types of plant produce significantly different concentrations, so we can’t assume too much about the result of completely alien biology.