John:
You can get some 5000 grit wet sandpaper at an automotive body supply shop. While there, get a clay bar. The 5000 grit feels almost like notebook paper, not much more grit than that. Ask the guy at the counter to show you how to fold the paper, it is important since it will be getting wet and incorrectly folded will be hard to manage.
With copious amounts of water, and a very light pressure, you can wet sand the oxidation down very slightly to get a smoother finish to move to the next step. Ultimately you want to get it acceptable to apply wax/sealant. After the gentle wet sanding, apply the clay bar, equally gently, to knock down the oxidation just a little further. This too must be used with a lot of water. After these two steps, apply some Meguiars #7 show car glaze, by hand, paying close attention to the directions on the bottle. Use many clean rags. If the #7 is not giving you a good sheen, you may have to go down to #2, then back to the #7. After the #7 go down to a finer polish like 3M Perfect It. After all of these steps, apply a good wax. My favorite, at least for now is Meguiars Tech Wax. This wax goes on and off like a dream and holds up beautifully.
I know this all sounds daunting, especially when we are talking about a 40-year-old patina. You can try it on a small inconspicuous area first. What you are removing is the oxidation (irregularities) not the paint. Shine/gloss comes from the absence of irregularities.
Surf some sites like Autogeek.net and superiorcarcare.net to learn a little bit about the latest and greatest products out there. Talk to the person at the auto body shop supply counter (look in your phone book). These guys see it all, and get feedback from the professionals on what works and what does not.
You can always work backwards from my instructions above to see what may work and be less aggressive. From an internet picture it is hard for me to discern the level of your oxidation. I can tell you though, that paint that is cracked/checked/crazed can be made to look better. Not perfect, but better. You can try to start with the #2 Meguiars instead of the wet-sand and work down from there. More elbow grease, but a potential path. I have been doing this for so many years that I have learned to let the products work for me (many grades of polish, air driven polishers, special pads, etc). Old-fashioned love and muscle can do just as good a job though; it just takes a little longer.
Good luck,
Ed Fisher
Dallas, Tx