In that case you need to not only keep in mind "a problem, aka something broken," but the idea that there might be a wiring error in the new harness
As I said earlier you need to pull the switch out and probe the connections with the switch connected and turned on. This will load the system and if there's a poor connection, cause the voltage drop to show up
Part of this problem could be as simple as a poor connection at a fuse (not the headlamps)