2. 'Pink-eye'

No, I’m not breaking out my medical kit to cure your conjunctivitis.
If a red-eye is a long overnight flight, a pink-eye is any flight just short of that.
For the purposes of the airlines, a red-eye is a flight that touches the 1 a.m. hour, so a flight that goes into midnight but narrowly escapes the next hour could be defined as a pink-eye.