I had the same problem on my truck one time with a set of aftermarket LEDs. Same issue-When I was in reverse, I didn't have brake light, turn signal, running light, etc. on the passenger side. It was caused by one of the connector pins didn't seat correctly and got shoved out of the connector. I had to continually glue that pin back into the connector cuz it kept getting shoved out, until I finally decided to replace those junk taillights lol
It sounds weird, but I believe mine was the ground wire that wasn't connecting properly. I don't know why, but everything else worked despite that taillight not being properly grounded