Brake light issue

I would check for a bad ground. You can use a jumper wire to add a ground to the light to test if you have a ground problem. If the light works when you add a test ground. The I would start looking for corrosion around the wires and at the factory grounds

Looks like they spliced in for trailer wording also

I would start their and make sure all connection are good

Check if the insulation on the wires is scratched down to copper and touching the body or frame.

Sometimes trailer harnesses are spliced in with 3m blue clip locks. These sometimes don't get a great connection. If this is the problem, buy a new clip and re do the connection. Hope this helps.