I'm glad your in the loop on what it takes to do a BCM in a car these days, sometimes it can be tricky understand. Well, other than checking bulbs (first thing is first), and you've checked all the fuses already, the next step would be to do some pinpoint circuit testing. I'll warn you in advance, this is not easy, it would really help if you have an automotive test lamp with a sharp probe. If not we might be able to make due with a multi-meter.
Please let me know if you have any questions for me prior to proceeding. Since there is specific testing involved I'd like to know you're comfortable with the above steps and tools necessary for accurate diagnosis. If so I will lay out the procedures and you can report back your findings.
Simply put there are 2 wires coming out of connector X1, which plugs into your multi-function switch and travels to the BCM. The wire for the left signals is light blue and white. NOTE: there is a DARK blue and white wire as well, this is for the Right turn signals. These wires give the BCM a ground signal when the respective side is activated, telling it to start blinking, so this is what we need to test for. With a test lamp hooked up to battery positive on the clamp end, any ground touched by the probe end will illuminate the test lamp. Be careful not to stab yourself when piercing the wires. Also you probably guessed this already but this test must be done with all the connectors plugged in, as if the vehicle was operating.
Again, please feel free to ask any questions that come to mind. It is my goal to detmine the cause and remedy for your concern. I look forward to a speedy repair! Thank you.