I used a snap action switch in 1987 with the rear brakes when my bike trailer was in the planning stage. I excluded a brake light on my bike.
Center-pull calipers had the brake switch mounted on a bar on the rear forks above the caliper, activated by the equalizer bolt or a separate bolt on the cable.
Side-pull calipers had the switch attached to the lower caliper arm, activated by the upper caliper arm to illuminate the rear brake lights on my trailer.
As I am a newcomer to this site, I couldn't post photos of my trailer connections. I still have my legacy bike trailer, stored over the winter.