A every representative of a given morph should have the same mutation at a given locus (with some notable exceptions, like Albino), yes. But, to be able to confidently call the specific mutation requires a statistically significant number of individuals that carry the mutation being interrogated to ensure that the change at the genomic level that is found is consistent. Given the number of “silent” mutations that occur across a genome, if you only looked at a single representative of any given morph, odds are you would not be able to call which of the many small changes you found was the absolute source for the mutant phenotype