Blinking and squinting on pecking and with drowsiness
A striking feature of some birds is that they blink when they peck. With each peck, just before the moment of impact, the nictitating membrane deploys. Examples are provided in a chicken (Gallus gallus domesticus) and a domestic turkey (Meleagris gallopavo).
Four pecks associated with nictitating membrane blinking in a chicken, played at 10% speed.

130ms after the head begins to move and immediately before the beak strikes the fruit coated surface, the nictitating membrane deploys. The lower lid also rises a little.

Blink on pecking in a domestic turkey. The nictitating membrane appears 200ms after the head movement begins.
Zebra doves (Geopelia striata) also blink on pecking, but using the upper lid as well as the nictitating membrane.

Brief upper lid blink on pecking in a zebra dove. It is first seen in the 40ms frame and has ended after the strike, in the 160ms frame. If you look closely, it is possible that the eyelids retain a small gap between them even at maximal blink.
Upper lid blinking on pecking in a laughing dove (Spilopelia senegalensis). Played at 20% speed.
Crested pigeon (Ocyphaps lophotes) squint on pecking

The upper and lower lids have come together while pecking and the pupil is visible
Zebra dove (Geopelia striata) squinting during pecking

Wonga pigeon (Leucosarcia melanoleuca) squinting while drowsy.

The upper lid descends, then the lower lid rises to meet it, the (palpebral) fissure between them moves up and down. In the bottom left picture where the bird is squinting, it is unlikely that this is improving the depth of focus as the nictitating membrane is across the eye.
White-headed pigeon (Columba leucomela) squinting while drowsy

The upper lid descends, then the lower lid rises to meet it, the (palpebral) fissure between them moves up and down. Again, although the bird is squinting it is unlikely that this is improving the depth of focus as the nictitating membrane is across the eye.
Bush stone curlew (Burhinus grallarius) squinting while drowsy
The nictitating membrane crosses, the lower lid rises, the eye wobbles (saccadic oscillation) then the nictitating membrane withdraws and the squint persists
Tawny frogmouth (Podargus strigoides) squinting while drowsy
The lower lid rises slowly until the palpebral fissure is reduced to a slit. The pupil remains visible. At the end there is an upper lid blink.