I understand thus far that it could be the wiring, the fuse, or the turn-signal switch. Since they both went out at once, it's probably not the bulbs.
I checked the headlight fuse in the engine compartment and it looks fine. I cleaned it with electrical cleaner and still have the same issue.
As for the switch, the blinkers high-beams and parking lights work fine.
Are places like AutoZone and Advanced Auto Parts able to test fuses for you?

What is the most efficient, practical, and linear way to approach this issue?