It might not be a problem with the trailer.
Many recent vehicles have separate fuses and relays for left, right turn signals and tail/marker lights.
For example, my wife's best friend has a 2008 Ford Escape. She borrowed my utility trailer to moved some stuff, but the lights would not work. I looked into it and found while her SUV had all the fuses, it did not have the 3 relays. I found the relays at etrailer.com for about $25 total. I put them in for her and now the trailer lights work great.
From what I heard, the relays run about $30 each from a dealer.
FAA A&P mechanic, ex-RV dealer parts dept
Retired B-52 Gunner/Flight Examiner, B-52 Crew Chief
2016 Jayco Eagle HT 29.5 FBDS w/ 15,000 BTU AC, 50 amp service, upgraded counter top, thermal pane windows, elec. stab jacks, outside grill, backup camera and MORryde pin box.
2011 GMC 2500HD DURAMAX/ ALLISON