Probably quite a separate phenomenon, but if I wake when it's still night and I want to know what time it is, I'll often blink my eyes open for a tiny fraction of a second to see the glowing alarm clock. I often don't know what time it is until I "read" the time from my memory. (It's either my memory or the after-image on my retina.)
During my Ph.D, I would often spot this on my way to the lab. I would be seated in the subway early in the morning, and suddenly realize that the name of a station had just been announced, but that I hadn't heard it. Then, it was suddenly like I had heard it -- as if the trace sensory signal in auditory cortex had been isolated and amplified by my attentional system, before it fully dissipated.
It was (and still is) super cool.