The sensors that shorted out weren't related to the fuel tank. They were all in the engine. The problem is— like you said— one warning light is used to signal too many problems. From this experience I'm getting the sense that I will disbelieve "It's probably the fuel cap" next time unless there are also obvious signs there's a fuel cap problem. For example, on a previous car the "CHECK ENGINE" light came on one time while I smelled gasoline from inside the car while driving. I pulled over, checked the gas cap, and found it wasn't sealed tightly.

OTOH the problem of too many things connected to one warning light could be solved like our BMW, which has too many warning lights. The owners manual has several pages of rosetta stone translation to help decode what dozens of hieroglyphics that can be displayed on the dashboard mean.

Actual conversations in the car have gone like this:

"There's a light on."

"Which one?"

"On the dashboard."

"Right. What does it look like?"

"It looks like... a bomb, frankly."

"Like a round bomb with a fuse on top, from Tom & Jerry?"

"Yes."

"Are there wavy lines around it, or no?"

"Yes, wavy lines."

"Are the wavy lines on the bottom, or on the sides?"

"Bottom."

"Is it yellow or red?"