Replace the bulb would be my suggestion. Start with the obvious.

 

If both don't work, its likely something that controls them. Its either the switch (easy and cheap) in the turn signal stalk, the relay, (easy and really cheap) or the worst scenario is the FCM (Front Control Module, neither easy nor cheap).

I had a similar scare, but mine turned out to be a chipmunk that ate through the wiring harness behind the inner fender cover. Took months to diagnose, but was an easy patch.

If its the FCM, then the best thing to do is find a sympathetic dealer, that can recode a used one to the car. I bought a used one on ebay for 100 clams.

 

lol reminds me of the time it happened to me. No low beams one night , great i said more money into this truck for new dimmer switch.
Then I decided to try the bulb. turns out both bulbs were blown.

 

If it turns out not to be two bulbs blown at the same time (it can happen, when one blows there can be a surge), it is likely the multi-function switch. YMMV, but for me, I started to take apart the column to replace mine as I had a used one from the GEN3.1 Dakotas on hand for replacement. Turns out that the GEN3.2 Dakotas (2007-) use a similar but different switch. In the old ones all of the power went through the switch, in the new ones, it is only signal that goes through. I disconnected the switch to see what was what, then had to reconnect since I didn't have a replacement. Click! All Better, 3 years later, it still works. Must have been some kind of re-boot, so try that.