Is there a rule to calculate the correct voltage for a light bulb?
Rated voltage is chosen or defined based on material and/or component properties and also on endurance tests of multiple samples.
Therefore, without knowing what's in the "black box" you cannot know the rated voltage.
Without having a number of samples, you cannot know test/deduce what the rated voltage is.

E.g. different LED's with the same voltage rating (can) have different intensities. If you apply the rated voltage to a ultra bright LED and apply an overvoltage to a 'normal' LED, they may have the same intensity. But the normal LED may get damaged due to the overvoltage.
So, checking the intensity of LED's cannot be used to trace back what the rated voltage would have been.