When I lived in south Texas I had flour tortillas lightly toasted on occasion, but most of the time they were taken and used cold from the package, and breakfast tacos, burritos, or fajitas assembled from them. I think the local distributors baked them just a tiny bit longer than some companies do, so they wouldn't really be "raw" tasting.
Incidentally, in Texas I saw few Mexican-Americans eat corn tortillas unless it was at Taco Bell. At regular restaurants, almost everyone had flour tortillas for bread. There, as you see in many Mexican restaurants, they are served in a covered bowl, lightly steamed. Kind of pasty to my taste.
It wasn't until North Carolina acquired a larger Mexican population that I experienced corn tortillas cooked on a griddle. The first time, I stopped at a restaurant that had tongue tacos - "lengua" - and ordered a plate. Each taco was served in two corn tortillas browned on their griddle. I was hooked.
At home, I soon tried to duplicate this but didn't have much luck. The corn tortillas, almost raw in their big bagged stacks (nice and inexpensive) from the regular groceries, which had began to stock them, got hard and leathery on my frying pan. Not good. So for a while I eschewed them and either fried my corn tortillas or ate flour tortillas.
Eventually I learned the trick. Here's how:
To make four tacos, since I was impressed with the double-wrap technique using corn tortillas, place a stack of eight on the griddle. I use a big cast iron frying pan. I also brush both sides of each tortilla with a little mix of a spoonful of water and some olive oil before I start. I don't want much oil, just a tiny bit.Place the entire stack of eight in the hot pan. On medium heat, the bottom-most corn tortilla, #1, browns on one side, just right. I flip the whole stack over with my spatula, keeping the stack lined up nicely, and begin browning tortilla #8. Then with my thumb and forefinger, I flip the done side of #1 which is now on top, over, exposing the uncooked side. When side a of #8 is browned, I flip the stack, begin browning side b of #1, and when it's done, flip the stack again, and brown side b of #8. At this point, like you, my mind begins to wander and - pay attention now!
At that point, I grab tortilla #1 and #2, and flip them both over. I then flip the whole stack again. #8 on top gets flipped along with #7. Now, both #1 and #8 are headed for the center of the stack.
So on, finishing #2 and #7, and then turning the top three. Bringing in turn #3 and #6 to the top and bottom of the stack. If you are counting, that's 16 flips to get them all. Note that if you cooked them one at a time, you would still have that same amount of flipping to do. The process of dealing them into the pan will be reduced to once.
The advantage to all this, is that as the stack begins heating up, you are steaming the tortillas. The browned portions of your stack, as they are moved towards the center, lose their leathery dry texture and become quite tender.
Eventually the last, tortillas #4 and #5, are browned on both sides. You are ready to remove the whole stack and stash it in a covered bowl and assemble your tacos, or fajitas, or what-have-you. (Slices of Texas-style slow cooked brisket come to mind.)
Once you master that, you can do your flour tortillas the same way. By the way, I never use a double-tortilla if it's a flour tortilla.