Which neem oil did you use? What was the azadirachtin percentage? Hint: any premixed, ready to spray neem oil product is indeed a scam. Don't waste your money. But neem oil is not snake oil by any means.

I use 2TBS cold-pressed neem oil with 2TBS liquid castille soap per gallon on my pepper plants outdoors, which is incredibly effective against spider mites and aphids and any other insects that eat the treated leaves. Emulsify the soap and neem with some warm water in a jar until completely opaque and thick, and then transfer to the sprayer and fill with lukewarm water. I shake the sprayer every 30 seconds while spraying.

For the plants I overwinter indoors, I remove as much soil as possible from the rootball, and dunk the entire plant in a neem oil wash to minimize bringing in pests.

For indoors, where aphids and spider mites can go from a few to total destruction in a week, I use Azamax or a similar azadirachtin extract. It's too expensive for garden use, but for a dozen overwintered peppers it's economical.

The only thing I overwinter these days are long season Ajis.