Gerie, a suggestion: go to a local mexican who imports cars into Mexico regularly (all kinds, not only pickups) and pay him/her either a fee to do it for you completely, or a smaller fee to guide you through the process up there at the border. Also, the brokers up there make it pretty easy and safe for you to do: they're hooked up to the aduana's computers, etc. in the capital, and they're issued an importation number & the related paperwork for every car they import, right at the time it's being done; with you standing there. So it's relatively safe. (as safe as things can be in this crazy bureaucratic country).

There's lots of mexicans importing cars, trucks, vans, from the U.S. these days, to make a few bucks on them down here. I've befriended two different ones here in my neighborhood and when you know what you're doing (like they do) it's a breeze to import anything from the U.S.
Well, when I say "anything", I mean cars & trucks & minivans from the 80s and 90s and 2000s. I actually don't know if there's some special restrictions on vehicles from the 60s. I will ask one of my friends. But I've been watching them for years, bringing lots & lots of vehicles down here from the U.S. Of course they're given Mexico City tags before being sold to the next owner here.
I personally have only done it twice: once with a seven year old car, and once with a six-year-old Harley. Both went fairly smoothly, especially at the border where of course I used a broker. Within 40 minutes the broker handed me the temporary title showing duty & taxes paid directly to the government agency in mexico city, and said "your vehicle is now Mexican." The local mexico city "DMV" of course issued a totally different, permanent title. Neither procedure took the original, California title from me: I still have that.