What would it take to spark through electrical tape?
You're looking for the dielectric breakdown voltage of electrical tape. For this 3M brand it's 10kV.

So, if you get to about 10,000 volts, it'll spark through. For the equivalent thickness of air (0.216mm) it would only take 648 volts to spark.

Once it's been sparked through once, the insulating properties for that spot are probably greatly reduced. It'd require much less to spark through the same spot again.

The resistance is another matter. It's rated at 1e6 megohms, so some very very small current will flow at any voltage.