The exact error can be seen by using the menu button then scroll down to select "Stored warnings". In my case, it showed error relating to third center brake light. Note that the display panel must display "ready" to use this menu. Press the right control button on the right steering column stalk as needed to cycle the display to this state.
Google search indicates that this is a common problem relating to wiring on Fiat 500 series. However, in this case, it seems to be a manufacturing error.
A simple volt meter check showed that there is 12v pulse present when I pressed the brake pedal. I removed the light and checked the individual LED and associated component (in circuit test) and they all seem to be normal. At closer inspection, I found that the terminal was not soldered properly (actually not even soldered!). The picture below is what mine was before repaired.
I have additional pictures of disassembling step taken after I repaired the unit. You will need a needle nose pliers, standard Phillips screwdriver and a T-10 torx driver.
Remove the rear brake light housing. Use a small prying tool to remove the screw cover then remove the two screws. This piece has 2 additional snap pin holding it in place so it won't fall off after the screws are removed. You will need to gently pull on the 2 ends to pop it out.
Use the needle nose pliers to remove the wire connector.
Use the Torx driver to remove the light.
Inspect the solder connection and remove the circuit board from the light housing to repair. The plastic housing is soft so the board should pop out easily with some light prying. Note that I did the solder repair already when this picture was taken.
After repair is done, just assemble in reverse and the warning light should go away.
