Fanon Light type Pokémon appear to be prominently some sort of "holy" type, somewhat like the Fairy type but more serious and less cute. A good bunch of them are largely based on the concept of hope or good will. But sometimes, the Light type is taken too literally, being based on illumination instead. Rarely, both of these concepts are thrown into a Pokémon.
In some other games, it can also be associated on freedom, as seen in Mighty and Nasty versions, and are not all good. There is even an usually evil Pokémon called Vitalight. However, in Gen EX and Gen EX 2, it is ultimately another elemental type similar to Fire, Ice and Electric instead of goodness, and avoid the common cliche of Light and Dark being Super Effective against each others.
Many Light Pokémon based on animals are also good-hearted, a symbol of hope or something similar to either concept. Animals not based on hope or goodness are usually the ones that prominently have or use illumination, for example to lure in prey like anglerfish. In Pokémon Mighty & Nasty and Pokémon Progress and Regress, the latter concept is far more prominent, but the former concept is sparsely used and not non-existent.
As time passes, Light as a fanon type was more based off goodness as a direct counterpart of the Dark-type (named "Evil" in Japan), even if some of them are more based of illumination. However, a few users like Samtendo09(t∣b∣c) prefers to make Light as an element, and not goodness, does to the fact that "good light vs evil darkness" had become too common nowadays and to avoid being too similar to Fighting and Fairy in a way, as well as allowing a proper Type that can act as a "Good-type" toward Dark-type.
That said, a mix of both (the holy/good version and the elemental version) can also exist in a few other fanon medias.