All of the above appear to be variation of two amino acids correct?
First of all, the genetics of eye colour is a lot more involved than just two codons. There are also more colour variations than you described. You can start here to learn more about it.
I wonder what would happen if some of those amino acids had mutations that changed into any of the other 18 new amino acids???
If the codons you described play a role in the determination of eye colour then it might have an effect. The gene those codons are in might not work any more, so it might mean that eye colour would be influenced in some way. It's hard to tell what would happen without knowing which of the many factors that determine eye colour we are talking about here.
Am I right in thinking that mutations at the beginning of each condon would more likely result in larger mutations? Or would the eyes start to lose some particular functions?
The mutation of a single nucleotide may or may not result in the coding of a different amino acid, regardless of which nucleotide of the codon is affected. You can verify this yourself if you study some tables listing the codons and their associated amino acids. The effect of such mutations can be anything from no effect at all to quite significant, because it depends entirely on the effect of the new amino acid on the protein it's part of.
"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.