I'd start by whipping out a multimeter, and checking resistance between the contacts on that plastic film, for that bulb and one of the others (of same type that should be on at the same time), to make sure the circuit isn't broken before it gets to the bulb carrier. If the contact is just dirty, you could try abrasion with a dry paper towel, or with rubbing alcohol on it, or a very mild abrasive like toothpaste. If the circuit to it is broken, you could solder a jumper wire from another bulb's contact to that one, matching the same polarity. I mean using a very fine wire to the bulb carrier contact, then reinstalling it, not to the plastic film contact pad because it may not tolerate that much heat.
Next I'd look at the bulb carrier's contacts, maybe they just need a cotton swab with metal polish or toothpaste to clean it off. You can use a multimeter to see if there is resistance between those two bulb carrier contacts (going from one carrier contact, through the bulb filament to the other one). If not, as a sanity check, I'd try a different bulb in case that one was blown new out of the package. Backing up, before I removed the bulb, I'd look very carefully to make sure it had been twisted all the way in. If not twisted all the way, maybe it didn't make contact with the plastic sheet contacts?
