just went through a similar situation with my buddy's 54 chevy custom.
it is using 6, 59 cadillac bullet tail lights, [three on each side, frenched into the fenders.]
as he is using the original 54 turn signal switch and wires, he added relays at the tail lights because he figured the multiple tail lights would be an excessive load on the original turn signal and brake light switches.
adding a relay to each bank of rear lights, every imaginal wiring combination of the relays would not make the rear lights function as they should. he would get brake lights on one side only, turn signals that would work one side or the other, but not both, or act as 4 ways, and other goofy combinations of both side rear lights.
i investigated his wiring, and it "seemed" the relays were wired correctly, and i even tried a couple of different ways to wire the relays, including using the ground to activate them. nothing worked. these were good quality bosch OEM relays.
sometimes, the relays would just "hum", and the lights would do nothing.
so just for grins, a pair of 1157 sockets were wired into the rear light harness in series with the caddy tail lights, and now the lights work as they should !
it seems there wasn't enough draw through the relays to trigger the flashers used in the turn signal and 4 way circuits through the original turn signal switch.
adding the extra 1157 bulbs in the tail light circuit[s] brought enough draw to allow the turn signals to work correctly, as well as the brake lights. [even though conventional wisdom would say using the three 1157 bulbs on each rear light circuit should be enough draw to trigger the flasher]
i have never ran into this before, but am tossing this out there for others to learn from, if having troubles in this area.
there are no issues with excess heat in either the tail light wiring, or the relay wiring.
he is going to mount these extra bulbs and sockets behind the upholstery side panels in the trunk, close to the 1/4 panels on the rear of the wheel tubs.
i couldn't believe how this problem needed to be fixed, but i wrote it down for future use.