Part of this question is predicated on the idea that light bulb jokes are anywhere near as old as the modern incandescent bulb, which I would likewise have guessed to be true. However, the jokes seem to be several generations younger. Most commentary on these jokes puts their rise squarely in the 1960s and 1970s, reaching full efflorescence (or fluorescence, but that's the wrong kind of bulb) in the late 1970s. A couple of discussions reference, and anecdotes seem to support, Alan Dundes's short piece "Many Hands Make Light Work or Caught in the Act of Screwing in Light Bulbs" in Western Folklore in 1981. It was part of an ethnic-regional joke cluster, and much more literature exists on some of these targets instead of the format of the joke itself, especially in the case of the many crude anti-Polish-'othering' gags. Even if the joke originated before the late 1960s, it only appears to have really taken off in the 1970s. So any analogue to the light bulb joke would reside among any number of threads of older racist, sexist, or similar humor, although I've seen nothing quite so programmable as the light bulb joke. Similar plug-in othering jokes, like 'what do you call a person with (whatever debility, sometimes in X circumstance)' seem to be of roughly the same vintage, but I'm not sure if that's just a coincidence or if there was some fad of lowbrow joke parallelism.

Of course, I may just be up a tree on this. /u/itsallfolklore would be the natural person to know more about it.