Now raising of the third eyelid isn't really a worrying condition or a sign of particular disease alone. Instead it can be seen as a normal part of his body's functions or it can be an extra feature of a range of conditions. But if the eyelid is up all the time in the absense of any disease in the eye (as sounds to be the case here), then we have to consider that this is a sign of nerve damage, nerve disease, or systemic illness.
In regards ***** ***** based disease, we do see raising of the 3rd eyelid with neurological conditions of the Vagus nerve (aka Horner's syndrome or Haws). This can be seen alongside dissymmetry of the pupils and it would be worth having your vet perform a neurological examination of his cranial nerves if you were to see any variation in his pupil size under even lighting. But as you noted no unevenness, we can hopefully be less concerned about this at this point.
In regards ***** ***** disease, we can see the 3rd eyelids raise with any illness. If he has been otherwise normal then this might be less likely (or there could be something brewing at this stage). The reason I asked after the state of his stools, is that we can also see that and elevated third eyelids as part of the pathogenesis of a strange little virus called Torovirus that will cause a self-limiting condition of diarrhea + 3rd eyelid raising. In his case this sounds unlikely but it is worth keeping an eye on Teddy's stool.
As well, we can see the 3rd eyelid become prominent if he is has been on the border of developing an illness (ie upper respiratory infection
or gastroenteritis). The reason for this eyelid response is again really known, but it is thought to be related to decreased sympathetic tone associated with these illnesses. So, if he has had no primary eye issue or changes to his stool; we do need to keep an eye out for a brewing respiratory to GI bug at this stage.
Overall, to see this sign in an otherwise healthy cat, we'd usually advise to monitoring him at this stage. If he is eating and drinking normally with good hydration, then there isn't really an indication to test/treat him (since it is more a message then a disease itself. Still, if you find this persists and doesn't settle within the next few days, then we'd want to consider a possible check up with his vet at that point. They can test his cranial nerves, his eye, and underlying disease can be confirmed or ruled out. Depending on their findings, the primary issue found may need treating but at the moment with only this to go on, we would need to monitor Teddy to see if this settles or if it is a clue of something lurking that we do need to address.
Please take care,