Directional Flasher

That hanging cylinder is either the directional Flasher or Hazard flasher. They make the click sound when the lights flash.

That looks too small, looks more like the time delay. There are two flashers and they are interchangeable. Hazards are powered at all times, the signals must have the key in "run."

You need a service manual. Download one, free from MyMopar.

What fuse services what is detailed in a chart/ listing in the back of section 8 just before the wiring diagrams begin.