I have some nocturnal animals photos from Australia, taken with a flashlight or occasionaly internal flash. This rendered the pupils with all shades of yellow and purple:
So far, the best I could do is use an RGB curve (tone curve would probably also do) and with parametric + over the eyes drawn mask basically push everyting but the furthest whites all the way down on multiply. Often, I need to use multiple curves to a) get it dark enough if I increased exposure and/or b) to bring back some catchlight. I also desaturate the colour over the eyes (same mask). After that, I mostly need to retouch some of the said catchlight, which works sometimes ok-ish:
Anyway, whether it works or not, this is not an ideal workflow and is very time consuming - and I have maybe a thousand of such images. All was shot handheld, so I cannot use the exactly same masks and retouches even on bursts.
If it was red eye I would use the color zones module to desaturate and darken the reds, but your possum eyes are a whole different problem . The girls eyes were done in DT using color zones. The possums eye was Lightroom using animal eye correction. Even it struggled. Gimp was unable to do the red eye correction on the possum eyes although on a person it works fine.
EDIT: If you put a diffuser or white material such as a tissue over the flash you may reduce the pet eye effect when taking the image. Also an accessory flash placed away from lens should eliminate or reduce the pet eye effect. It would be best to sort this problem in the camera. Red eye and pet eye is caused by the flash being too close to the lens.