Cat's eye third eye lid issues....dont close

My elderly  female cat is 16 years old...I would say she is late 80s/early 90s -like in human years,

Being treated for hyperthryroism  with taperzole for 5 years now

It seems when she sleeps her third eye lids do not close, so she looks like she is sleeping with her eyes open. In retrospect, it seems this has been going on for 1-3? years.

She often has that sleepy,red eye look like we get when we have been up, say 20 hours non stop.

Any thoughts?

I had a cat that slept with her eyes open. It was very interesting to watch a rem sleep cycle.

Are there any other signs? Such as not eating, lethargy, temperature?

Thyroid drugs make cats do weird things.

The one I had couldn't stop moving. She actually got stuck one day because she didn't have room to turn and she couldn't understand how to back up. I had to take her off the drugs for a while and that was the only time she acted normal. When we went back on the drugs she started it again. (She was a rescue and we ended up putting her down, she had so many issues and had for so long untreated that we couldn't get a handle on it and she was just slowly dying. )

I'd recommend some basic saline eye drops for her to help keep everything lubricated.

And check with your vet to make sure they have no concerns but if she's been doing it for so long there probably isn't anything majorly wrong.