I finally found the little wire brush that is small enough to get between and clean each of seven sections of a trailer's seven-pin connector, so I pass this discovery along in case I am not the only one who did not know how to find them.
It's called a air-gun brush, or a paint-sprayer brush. I found some at Harbor Freight, but in the paint-sprayer department. (Thanks to Harbor Freight for directing me to the right department.) Amazon has them, too.
