I do have a spare fuel pump, but I don't bother with a spare tire anymore. I have had flats on three rallys. The first one was up in Sequoia National Park about ten years ago. My Micky Thompson's had almost no tread left and after running for four hours, two of them were going down. It took four cans of flat fixer to finish the rally (my friends gave me a couple).
The second time was on the Angeles Crest Road. I saw the sharp little rock in the road. It was in the middle of a sweeping curve, but I was going too fast to alter my course enough to miss it. The right rear just clipped it. I was hoping that the tire was OK, but at the next checkpoint, as we slowly rolled along, we could hear the psst, psst, psst. It was in the sidewall, too. One can of fix-a-flat got us to the end of the rally and home.
The third time was last year on the Eureka National TSD Rally near Landcaster. I was on my brand new Toyos and I ran over something that put a one-inch gash in the inside sidewall of the right front. It took two cans to finish the rally and two more to get home. That stuff is great, I should buy it by the case!
I also carry tire plugs, but so far they have stayed in the trunk.
Paul