Do not plug the tire, have it patched from the inside. The only thing to keep in mind when patching these Goodyear Run-Flats is that they can only be patched twice before Goodyear deems them as unuseable. Each time you patch the tire it goes down one letter in speed rating. For example, a Y rated tire (186 MPH) drops to a W rating (168 MPH), and a W Rated tire (168 MPH) drops to a V rating (149 MPH).
Some other manufacturers say their run-flats cannot be patched and still keep their integrity.
I picked up a few nails in the EMT's I had on my Corvette, those tires were patched with no problem.
I picked up a nail in one of my F1 run-flats, had it plugged externally, and have driven many thousands of trouble free miles. I have had many external plugs in many different kinds of tires over the years and I have had only one plug that would not seal properly and ultimately required an internal patch. The fact is, with run-flats a failed plug is not as critical as it is with a non-runflat. A failed plug is really no different than picking up another nail. If you have run-flats, you can keep driving whether it is a failed plug or a new nail. While a plug might have an effect on the speed rating, I don't think integrity of the tire is an issue in this case. The tire is not going to disintegrate, wreck your car, and kill you because of a failed plug.
Some manufacturers of runflats won't allow their tires to be repaired since they don't know how long they were run deflated prior to the repair. Attached is an article I just read in Road & Track about the newest Pirelli all-season runflats.