This isn't a typical "spider" issue and the 2010's are not as likely to suffer from that particular problem as the '06-'09. Not to say they can't but it probably isn't the first thing I would check. (If you are ONLY having issues with the signal lights, I would certainly focus on that part of the system first) In most issues with the multi-pin spiders, all sorts of other weird stuff happens - no windshield up/down, high beam indicator on, glove box solenoid inoperative, possible no start, signal indicators often both lit (faintly) etc.
Check the handlebar switch first. Take it apart and clean it up.
Have a look at the sockets for the turn signals - the front, in particular. (Potentially more exposed but the rear is also possible.) A bit of a pain to get to but I think I would start by disconnecting the harness sequentially from the right and left front signals and see if the problem goes away. If it does, have a look at the connectors and especially the sockets themselves. Pretty common issue to have a short in a corroded socket so the blink feeds back to all of the bulbs. I have seen it before with two filament bulbs/sockets on bikes and cars.
Going to be harder to find if it isn't one of the above.
Note: It is normal to see slight changes in the front marker light element on the left side when the right blinker is going (not the blinker filament). I think this is just due to slight voltage fluctuations due to the current draw of the signal lights.
Edit - Have you done anything electrical to the bike lately? (added accessories/light etc?)