German made low voltage inspection lamp

Here is a very interesting device found on eBay. It is a small inspection lamp powered from a transformer built into a housing with a BC lamp cap so that it can be plugged into an existing domestic lampholder. There is no manufacturer's name, just the word 'Germany' and the supply voltage range of 235-250V, which I am guessing makes it pre-war. The lamps are rated at 15V but on measuring the output of the transformer it shows 25V so there may be some resistance dropping in the supply cable as the lampholder terminals do measure approximately 15V (AC).

Unfortunately, one of the lamps (the angled one) does not work as the cap is loose and I suspect a broken wire. I don't know if it's possible to repair..?