240 fps
I did an experiment, because I'm a scientist now apparently.
I propped my phone on the shoe rack at an angle, so it could see me and the mirror at the same time, and filmed in slow motion. 240 frames per second. Then I blinked twenty times.
Then I went through the video frame by frame. That took two hours.
Seventeen times, my eyes and the reflection's eyes close on the same frame. Three times, the reflection closes its eyes two or three frames after me. That's about a hundredth of a second. Light needs a few billionths of a second to go to the mirror and back. So it should be zero.
I googled for a while and found rolling shutter: phone cameras don't take the whole picture at once, they read it line by line from top to bottom. In my video my face is a bit higher up in the picture than the reflection. So the reflection gets read a tiny bit later. That's probably it.
It would be late every time then, though. Not three out of twenty.
It's 2am and I'm explaining rolling shutter to myself. Bed.