This is "QTL" by Arlan Andrews, published as Analog's "Probability Zero" column for February 1987.
"It was the term, faster than C, that finally revealed to me, in a flash," the physiologist said, "that there were phenomena quicker than light."
"Quicker than light?" the question sputtered incoherently out of the physicist's mouth. "What do you mean quicker?"
Eyes shut in photographs:
"Simple-we've all photographed our family and friends, and invariably the subject will have his or her eyes shut. How can this be?"
Eyelashes can pre-detect the flash:
We believe eyelashes act as antennae that discriminate among the ethereal vibrations, reacting to previously unsuspected precursors of light waves that travel ahead of the light wavefront
From which comes a space drive:
"And so, children," the Historian said, "we have the story of the development of the QTL drive that powers our so-called 'shadow ships' as they wink across the Galaxies
I can't quote any more, the article is scarcely more than a page all told. Hat tip to Dosco Jones for his clue (it is "Revlon Drive") from which I was able to find this.