It sounds to me like you have a bad ground connection. The voltage feeding the dipped beam lamps might be bleeding back through the high beam filaments and hence also the warning lamp due to high resistance on the ground wire or connection to chassis.

In your photos at the start of the post, it looked like the grounds were on the actual radiator. If this is so, it is not a good choice as it is rubber mounted to the body. I suggest you choose a better ground point on the car body. My car has threaded ground points on the inner wings near where the wiring for the main beams comes through into the engine bay.

Problems with vehicle wiring are caused by bad earths more often than any other fault!