Given that "epiphany" derives from "epi-" [on, above, to] and "phainein" [to show] I was wondering if there's any connection between the cartoon representation of an epiphany (a lightbulb over one's head) and the word.
Your question "Is there a connection" could be interpreted in a number of different ways.
Did the Greeks use the word epiphanein because the standard depiction is a light-bulb?
Do we use the word epiphany because the standard depiction is a light-bulb and the word seems to fit?
Do we a use a light-bulb because it's a good representation of what an epiphany is?
The first two interpretations are obtuse and the answer to both is obviously No. The Greeks didn't have light-bulbs; and we had the word epiphany before they were invented too.
The last question is probably off-topic, because you are asking about a depiction of a concept, as opposed to a description.
However, the answer to it is almost certainly Yes. An epiphany (when it isn't a literal manifestation) is a sudden realisation. Something not previously clear or known has been brought into the light of knowledge or comprehension. It is as though what could not be seen in a dark room has suddenly been shown to you by turning on the light.
Here's what the Online Etymology Dictionary says:
epiphany (n.) early 14c., "festival of the manifestation of Christ to the gentiles" (celebrated Jan. 6; usually with a capital -E-), from O.Fr. epiphanie, from L.L. epiphania, neuter plural (taken as feminine singular), from late Gk. epiphaneia "manifestation, striking appearance" (in New Testament, "advent or manifestation of Christ"), from epiphanes "manifest, conspicuous," from epiphainein "to manifest, display," from epi "on, to" (see epi-) + phainein "to show"
Look at this, too:
Why is the light bulb a symbol of a good idea?
No seems to be the answer to your question.
I think the basic archetype here is a universal cross-cultural association between knowledge and light. Christian saints, the Buddha, and the Hindu gods are all depicted with halos of light representing knowledge, wisdom, 'enlightenment', etc. Plato's metaphor of the cave is a good non-religious(?) example. Also the metaphor of the beacon.
Some idioms: a guiding light, a leading light, begin to see the light, bring to light, come to light, first see the light of day, in light of, in the cold light of day, see in a new light see the light, see the light of day, shed light on, etc.