What is this New insect eating my little sage plant (ARRGH!)

Ok, so far we've dealt with the dreaded mooshy super destructive pickle worm (starting new cukes from seed this week unless someone says hold off another week) & tobacco/tomato horned caterpillars - this week a new insect has hit the little beach garden.
It is eating my little sage plant bad! Haven't been able to see the offender but it leaves little black round 1-2mm droppings & cobwebby strands beneath the leaves & on stems. It really is munching away on the sage leaves.
I had bad experience using Dawn on the pickle worm cukes - maybe it was too concentrated & the vines were destined to die but my solution scalded my carrot tops, killing them, & my pole bean leaves - the plants recovered.
Anyone please - 1. What is this new insect plaguing the sage?
2. How do I kill it? Honestly the webby stuff entangled in the munched leaves & stems with the tiny black BB like droppings has me thinking darkly about the easy solution of Sevin. I hate the idea of killing indiscriminately though & as I want sage for fall cooking, hesitate a bit (though not too much b/c of the relatively low toxicity to vertebrates) about the Sevin. Still Sevin stuffed pork & fowl probably isn't what we are looking for.
Any IDs & advice really appreciated.
It seems the beach is a tough place to garden down here.

Look very carefully for small caterpillars. It that proves to be the culprit Bt will take care of it.

thanks!
Another question (always with the questions! LOL) - what is the proper concentration for DAWN detergent & water to go in a spray bottle so as not to scald my plants?

Aha! There WERE little worms in those cobwebby tents littered with 1mm or less black poops! I picked through the webs (they are gross like mini tentworm tents) & couldn't find a one. Then I mixed up the new secret weapon - just under 1 teaspoon of permethrin concentrate in a quart sprayer bottle & set to spraying. Witnin 2 minutes those little green worms (reminding me in color of those *&^%$ pickleworms I experienced in July) were out of their webs just a writhing on the poor chewed up sage leaves. It was deeply satisfying to smoosh every one of them. I cleaned out the webs & found several pupae cases those looked remarkably like brown curled up dead wax myrtle leaves & smushed them too. these creepy mini-tentworms even got into my thyme (now honestly what insect eats thyme for goodness sake) & rosemary - zapped them all to Kingdom come with my new best friend. The bottle has explicit concentrations to mix for different types of plants - less for cucurbite family members & the most for eggplant. it says you can apply up to one day before harvest on leafy vegies like spinach & chard - not going there. Will let herbs recover & grow out, way out before Thanksgiving harvest.
Permethrin - my new BF. Doing a third pole bean planting this pm - sticking with the rest of my Romanos b/c 2 planting of Vortex filet beans had poor yields in my garden. Also planting those FANTASTIC Burpee dual-purpose cucumbers again. In fairness I'll also put in some Armenian cukes but they had not formed fruit longer than my index finger when the pickleworms wiped them all out so I can't say how I liked them. Putting out zucchini again tonight too. (watch us get a hurricane in 3 weeks to tear all the new plantings out LOL).
Permethrin, friend of Stormy.