I'm pretty certain that the eyes aren't going to give away anything about lighting conditions when killed...it's an old wives tale....Your pupil isn't actually there, it is a hole in your eye, your iris is a system of muscles that contract or extend your lens and pupil to focus or allow more light, you'll note that if you're looking in a mirror close to your face, your pupils get large, however, if you look at your eyes in a reflection of another mirror in the mirror (increasing the length between you and your image) your pupils are smaller.

Anyway...your iris' are going to relax or contract following death, I would assume they would relax, but depending on the manner of death, they may contract similar to skeletal muscles going limp and the deer dropping, OR the deer jumping and convulsing violently after he's already "dead".

It is also possible that the deer isn't looking at the light the exact instant that it dies, say I shoot it and it runs 100ft, by the time it runs that far, it's eyes will have readjusted, or if it falls and dies relatively slowly, then the eyes will readjust during the death to the dark.

I would also assume that as the eye dries after death, the pupils will contract, since the total eye tissue will dry and contract.