In writing, you can take advantage of the differences in writing the two:
Look at the 2nd second of the video.
Look at the second sec. of the video.
Look at second #2 of the video.
If, in context, you have reason to refer to "the first second" (which only seems weird if you stare at it, and pretty much anything does that), you can follow with
Then, look at the next second of the video.
But in general I think "the second second" is fine. Especially in speaking rather than writing:
Look at the second second of the video
has a stress and tonal pattern on the first syllable of the first "second" that makes it quite clear.
It may look weird but sometimes the weird way is still the best way to write something — like some cases of "had had" or "that that".