If the orange lights worked the problem is in the trailer because both the red and orange lights are feed by the parking light circuit of the TV.
Did the parking lights in the stop lights work or just the small red light not working?
Generally Airstream run the wining down the center top of the trailer. The first place I would look is at the top 3 marker lights. Open them and see if you have power on the wire coming into any one of them. If you have power there you should be able to get that light to work by grounding it to the skin of the trailer.
If there is no power there the brake is forward of that point and most likely behind the interior skin.
There may be a chance they spliced both the front and rear marker lights at the distribution point in the front of the trailer. Look at the green wire coming into the trailer at the distribution point and see if that is a 2 wire or 3 wire connection. If 3 wires one should be the feed , the orange markers and the red markers. Test that connection.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles