Why won't my turn signal work?

Recently my front driver side turn signal bulb went out. It did the thing where it started blinking rapidly, suggesting the bulb was getting bad, but then it quickly stopped working altogether.

I took it to a mechanic who put a new bulb in, which also didn't work. He tried both the old bulb and the new bulb in the other turn signal bulb sockets, and both bulbs worked in them.

The mechanic said he tested the fuses and wire harness, and didn't find any issues there, and said I may need a new computer chip. Any ideas what else it could be?