pickup a "multi meter" you can pick them up fairly cheap at most large hardware stores or automotive stores in the electrical section. any were from 10 bucks to 100 bucks. a cheapy for 12v should all you need. and tag the ground and hot wires. for each side, and see if you get the same readings when lights flash.
i am going to say check your flasher unit, under the dash. i would have to look it up myself in how to test a flasher unit. with a multi meter, i have had one side go bad while other side works just fine.
if you have a trailer plug on rear of truck. run the new lights off of it. vs into the actual lights on vehicle. majority of factory wiring to tail lights on rear of vehicle or to the front turn singles on the vehicle itself, are smallest size wire they can get away with. and you could possibly over load the smaller size wire and burn it up / start a fire.
you may have a second flasher unit for trailer connector/plug, or perhaps a couple extra wires coming off of flasher just for a trailer connector. either or, the goal is splitting up how much electricity goes through a single flasher / wire coming off of the flasher.
with your notation of one side went completely dead. you may have left side and right side "fuses" and you might have blown the given side fuse. still would encourage double check flasher.
all the flashers units in vehicles in the past that i have had to replace have always been behind the glove box, on passenger side. and some sort of "removable panel" inside the glove box to get access to flasher unit. though i do remember a couple flashers being just under the dash. (remove under side panels and flashers right there) though that might have been a break controller or a diy job for trailer lights (way to many years ago)