Edit: it's important to use a scan tool to see what codes are stored in the BCM. This really should be the first step.
Tailights still have a circuit board, so there's a couple options:
1) Remove bulbs and run 12v to the each running lamp bulb to see if the bulb's bad (assuming you've already visually inspected the correct bulbs) as a confirmation to what you inspected.
2) use a testlight to see if 12v+ is being output in the bulb socket. This also has the added bonus of confirming the circuit board and wiring is good. You need to be very careful with this, especially since there's a circuit board involved. If you short the socket to ground, you may fry the board.
3) if you feel uncomfortable with #2, check for 12v+ at the input wires before the board (colors below).
As always, positive voltage is only half the equation. You also need to check that ground is good to both tail lights. (More below)
Tailight colors:
running lamp: white/orange
stop lamp: white/green
reverse lamp: white/violet
ground locations:
left taillight: left frame rail
right taillight: right frame rail
