It's very unlikely all three went out, especially given the long life reputation of LED's. I'd start by establishing how the trailer is wired. Are the three center lights tapped off of one of the tail lights? Left and right tail lights on my trailer are wired separately. You might look on Performance's website for a wiring diagram. Even with a test light, you are probably going to end up looking at the connector - is it one of those wire taps or is the wiring actually spliced?
A physical inspection will reveal a lot, though you may end up needing that test light after all.
Good luck!