The apparent cause seems to be the MC1R gene. In most people, that gene creates melanin. In redheads, however, the gene produces pheomelanin instead, causing red hair and fair skin. Another effect of pheomelanin is increased pain sensitivity, both for general and topical anesthesia.
Here's a research idea. Expose redheads and non-redheads to the cold pressor test, a standard laboratory test for pain using time as the dependent variable. Redheads, as a group, should remove their hands sooner.