The bulb failure circuit looks for an excessive voltage drop across the bulb sockets, which would normally occur when the bulb filament blows, but certain other things can cause it, too. You can get a voltage drop from corrosion and a poor connection at the socket, sometimes even if the bulb still lights. Try cleaning up the contacts where the bulb holder twists in, as well as the supply line where it meets the bulb holder contacts. Inspect the supply line in the exact spot where the bulb holder contacts hit it to determine if it has a pit due to electrolysis that creates a high-resistance connection where the bulb holder contact hits it; i.e., the bulb holder contact doesn't really physically contact the supply line very well due to the pit. If you can't correct this by bending the bulb holder contact so as to apply slightly more pressure, you will have to repair the supply line by cleaning it up thoroughly, until it's shiny, and filling the pit with solder. Do it quickly, with the corner of a well-tinned, big soldering iron, so you won't melt the surrounding plastic. Use only rosin core solder, NOT acid core. Then file the solder down smooth.

Also, a poor ground at one of the bulb modules can cause an excessive voltage drop.