If it was my ride I'd just put a camel hair "plug" in it. if you drove on the tire and it was flat you need a new tire. A car dealer replaces a tire if it has a puncture with in 1" of the sidewall. They also have to remove the tire and inspect it because people lie about driving on a tire once it's flat.
It's been weakened/compromised, change it. Those patches always fail in the end, and you would be worried about getting a blow out on the motorway all the time.
Plug it and see how it goes. Pay close attention to the tire (going down?) for the first few days. You won't get a blowout, but it may go flat again. If the plug doesn't work, you're not out very much.
A good tire place will tell you the truth if they can fix it or not. Sometimes you can put a plug in it, and it's like a new tire. Sometimes it's in a bad spot and they can't plug it.
If it's not leaking, I would leave it alone. If it's leaking, definitely change it... That's a bad spot to repair and in my experience plugs usually end up leaking in that area. I've driven many miles on a tire with a nail still in it that never went flat.
Honestly I think it's close enough that a plug only would do it. I had one that was maybe only an 1/8th inch inside of where your's is, and it didn't give me any issues. The tire is getting worn, plug it for a few months while you save up for at least a new pair of tires.
In the UK that can only be repaired safely by vulcanising. So it has to go off to a specialist firm. You have to weigh up the cost of this against replacing the tire. If there is a fair amount of tread left it may be worth doing. If not a new tire is needed.