I used to get an alcohol pad (the kind you use to prep for a shot) and wipe down everywhere you see scale. You can also use a paper towel and a bottle of alcohol. It does a few things. It physically removes all the adult scale, the crawlers (juveniles) and eggs and kills them. It also removes the sticky, sappy, sweet "honeydew" the insects poop out which the ants then eat.The ants don't bother anything anyway. Oil sprays work on the juveniles better than the adults so you'll need to spray a few times at maybe weekly intervals and then of course there are hard scale insects and soft scale insects. I don't remember which feed on pepper plants. Oil sprays smother scale insects so they can't breath. (through their skin) Their protective covering is a good defense.
If wiping with alcohol won't work bc the infestation is too big then you have to spray. Remember to spray weekly bc there will be eggs that hatch to replace the ones you killed. Use something like Pyrethrin (comes from Chrysanthemum flowers) or Sulfur or even Potassium salts of fatty acids. I also used to use Permithrin a lot (ok on food crops) Look at the active ingredient on the bottle of whatever you want to buy. I've never used Neem bc I was always supplied with commercial oil spray which I used at a rate of between 1% and 3% by volume depending on the temperature. That brings up my last tip. Never spray oil when its too hot out, like 90 or above. You'll burn the shit out of the plants and better to spray out of the sun. Good luck.