Whitefly eggs are clear color. Most eggs are typically in a more uniform pattern, if you know what I mean. Not so haphazardly as the ones in your picture.
You might want to check to see if back things are moving, maybe black aphids? Or flea beetles which are known to attack anything in the Solanaceae family which includes peppers. I see that there is also what looks like a white film in the areas where the black things are.
I'm at a loss. Let's ask
@mellielong if she can help you? She lives in the southern part of Florida, I think. Maybe she will have an idea or by some crazy chance she's seen them before.
Anything Woofie?