Plenty of experience in the same areas you mentioned, but I wouldn’t expect it to be easy locating an emergency/mini-spare. I suppose I’d call the junk yards directly, then a dealer.
But what’s more surprising is the defective emergency/mini. Never heard of that before. Deflated? Missing? Only 3 lug holes?
Separated tread with a sizeable air leak. Useless, in effect, but I drove it 3 miles to a friend’s place to save the tow.
Here’s thereason for the free advice: I wasn’t travelling out of state on some long desert highway, but all told from flat tire: About 40 minutes waiting on roadside assistance (I thought it was just needing air), 15-20 minutes moving the car to a friend’s, a half hour ride home, over 2 hour trip to pick up the only spare for my car in the state (which turned out to be blown), an hour to get my original tire fixed, a half hour (trip & jack time) to remount the tire, another hour to retrieve my wife to get both cars home plus another half hour to pick up the (smaller) spare with my bolt pattern (the ONLY other one in the state): >6 1/2 hours, all for a flat. I know it could have been worse, but this was ridiculous