I think you just need to get a good ground to your tail/brake lights. Your power is traveling through the left turn signal light filament. Finding no ground there is travels through the tail light filament of the same bulb and across to the right bulb. It still can't find a ground there but it does faintly light the bulb as it travels through both filaments there.

Make sure the light housings are grounded to the bed, the bed is grounded to the frame, the frame is grounded to the battery.

To answer your question about installing a harness, it's a fairly simple job on a truck like yours. But lights will still have to be grounded to work right.

"It's just a phase. He'll grow out of it." Mama, 1964

1956 Chevy 1/2-ton 3100
1953 Chevy 6100 "The Yard dog"
1954 GMC Suburban Now with a new proud owner.