You're describing the classic symptoms of a bad ground circuit. Signal lamp operation is different with the tail lights turned on or off. There's two clues you might be able to observe that will verify this. The first is if you look closely, you'll see the rear lights are not as bright as they should be. The second clue might not work here since both rear sides are affected, but turn on the left turn signal, then while it is flashing, remove the right rear signal bulb(s). If the left side stops lighting up when the right bulbs are unplugged, it is because the ground circuit on the left side is broken. Current goes through the left signal bulb's filament, then can't find a path to ground, but it doubles back through the smaller tail light filament, then over to the tail light filament on the right side, then finds an alternate path to ground on that side. You actually have three filaments in series, which is why the bulbs aren't full brightness.
If you can reach the terminals in the bulb's socket, you can take voltage measurements there too. Those readings are only valid when the bulb is installed, so you have to be able to get the meter's probe in there next to the terminals. With the circuits turned on, two of the four terminals on the common 3057 bulb must always have 0.0 volts. The other two will have 12 volts when they're turned on. You don't even have to concern yourself with which terminal is which for now. If you find roughly four to six volts on any terminal, that is proof the ground circuit has a break in it.
Jul 17, 2020 at 4:25 PM
(Merged)
