@cqctt - Welcome to the forum. Please take a moment to put your location in your profile, it adds context to your posts and allows readers to give more accurate answers to any questions.
Yes, both headlights should actuate as Nikolajsen said. There is a relay for the shutters, but I don't recall if there is a separate relay or fuse for each one. I no longer have a FSM to check. It's possible that it is just stuck or a wire is broken or loose somewhere. Check for the obvious and easy/cheap things first.
There was a headlight wire harness recall on your bike. The main issue was bulbs burning out quickly and the plug for the bulb melting due to a poor connection. The new harness has other improvements as well, like some larger gauge wires in places. Give the dealer a call and see if they can pull up your bike by it's VIN and tell you if the recall was done. The other recall for your '12 was for a fuel pump quad ring being installed incorrectly that could cause a leak. Most were fine, (my '12 was fine too), but might as well check if that got done too.
There are a couple of headlight lamp assemblies on ebay right now.
$76 LINK &
$136 LINK Cheaper than an entire headlight assembly at $477 or so from Yamaha. Yamaha does not sell the individual lamp assemblies.