First I would like to state that human genetics are very, very complex and we still do not have a complete understanding of them. For example, only relatively recently has the field of epigenetics made major advancementa, which (broadly speaking) studies how a cell's behavior can be changed WITHOUT it's DNA being changed.[1] This brings into question the age-old questions about environmental impact vs genetic impact in even greater detail. Anyways, sidebar over.

No, we are not completely sure how many chromosomes play a role in determining eye color. However, we do have a pretty good guess. Most recent estimates I found out the number at 16. OCA2 and HERC2 have the largest impact on eye color, but, there are many OTHER genes that also have smaller impacts on eye color. [2] That article I cited is actually amazing. But, it does touch on some more advanced subjects that are more introductory college-level biology or AP Biology than standard high school bio e.g. Gene Regulation, introns and extrons, etc.

To answer your more general question, in my (admittedly only mildly less basic, introductory college-level biology) opinion, it is unlikely that we will, anytime soon, reach a point where anything in genetics can be completly, 100% definitive. This is not to say that we haven't made amazing advancements in the field of genetics and biology more broadly. BUT, it would be a mistake to take for granted the complexity of the human genome. There is most definitely things we still do not understand about the genome, and will not for some time.

But, practically speaking, while other genes may have impact on some simple phenotypic traits, such as eye color, we can generally make an accurate guess based on only a few genes. In eye color, for example, one study was able to predict eye color with only 6 genes with about ~75% accuracy. [3]

The crazy part is, sometimes the genes that effect the phenotypic trait, don't actually store genetic material that determines the trait. In other words, they don't DIRECTLY determine the trait at all. Rather, the only effect ORHER genes which then effect the expression of the trait more directly. You can imagine that this could become very complex very very quickly when you have multiple genes effecting other genes which effect other genes, not to mention accoubting for environmental and demographic baises when doing these studies and you begin to see why this genetics is such a difficult field of study.

Apologies for the long post and rambling. Hopefully I was still able to provide you with some mediocre introductory-collage-level biology

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2791696/ [2] https://www.nature.com/articles/jhg2010126 [3] https://doi.org/10.1016/j.cub.2009.01.027