So, I've made some research, and I couldn't find any mention of azure garnets in the book. I've found one description of sapphires being azure, but that's nothing surprising. However in Chapter 5 of TWoK we have a mention of deep violet garnets: Also the books over and over again mention that 'something is garnet colour' (for example the Patternblade was this colour), so I dare to assume that all garnets on Roshar are indeed the same colour, but I may be wrong. As for that, it is kind of interesting. Because human blood is described as red or crimson (although Shallan once says her blood is purple in WoR, weird), so if 'bloodmark' would describe the colour of the garnet, then garnet's should be red, but the previous quote says they're violet. It is mentioned in WoR that axehounds' blood is violet, but I don't think anyone would actually call a gemstone after the colour of the blood of an axehound. So these 'bloodmark, clearmark, etc.' seem to refer more to their properties. Well, currently Shallan's eyes are blue. WoB states that each Order gest a different eye colour, so her eyes should change, as blue is the colour of Windrunners, and we all know Shallan is not a Windrunner. But what colour they should change into that is a good question. Should they be violet, red, orange (for Parshendi blood, because why not), or other colour? I don't know. I also have no idea, why her eyes did not change by now, as she said more of her Truths, than Kaladin sworn his oaths. I do see several possible explanations, though. Maybe she is subconsciously lightweaving her eyes to be blue.
Or it may actually be a general trait of Lightweavers. Lightweavers are already different from other Orders by having 'Truths' instead of 'Oaths', so maybe they are different also in other areas. Maybe they just simply have to say more Truths to get their eye colour. What I mean, is that how vague the Truths are as opposed to Oaths. The Oath you make and either you stick with it, or you break it, and you're not a Surgebinder anymore. The Truths can be either always true (like that when Shallan says 'I killed my father', because she can't change it in any way), or can be true at the moment (like when she says 'I'm afraid'). But if previously spoken Truth suddenly is not true anymore (for example if Shallan stops being afraid) is it like breaking an Oath? I don't think so. For me it looks like Lightweavers cannot break their Oaths, because they don't really have any. Maybe they just regress in their abilities when their Truth becomes untrue, and they have to say more? Well, maybe what I'm saying doesn't make a lot of sense to anyone, but what I mean is that having Truths instead of Oaths makes Lightweavers different from other Orders, and have to affect them in some way, and maybe (just maybe) it is somehow connected (in very complicated way) to their eye colour staying the same as it was.
Another explanation is that it may be just the 'state of mind' thing. I mean, at the end of WoR, Kaladin finally fully embraced his abilities and really started to recognise himself as a Windrunner, and maybe that's what caused the change of his eye colour. Shallan uses her powers, says her Truths, but even Mraize states at the end of WoR that Shallan still doesn't know who she is and she wants to be, so her eyes stay normal.
What I also want to say is that I know that WoB states that each Order has different eye colour. But was it mentioned that it is specifically the colour of the gemstone associated with the Order? Because if so, isn't it contradictory with the statement that all Knights Radiant had light eyes? Because the gemstone for Skybreakers seems to be Smokestone, which is described as black (definitely not light colour). Garnets being deep violet also don't sound like particularly light colour, because light violet is the colour of the Amethyst. And diamonds are completely clear. So what? White eyes for Edgedancers?