Here's what the wood of a real wood 65-66 woodgrain steering wheel looks like. It is made from 12 individual pieces, sanded and oil stained, no other finish, and I've kept it in a bag ever since. To get it up to a nicer condition, some 0000 steel wool and some walnut oil stain are required. This wheel was on the 66 GT Fastback I bought a very long time ago. I replaced it with a NOS Ford red wheel to match the red (code 25) interior back when a lot of NOS was available, then sold the car. It speaks Australian now (I hope it hasn't fallen off). I have a "restored" wood grain on my other 66 GT Fastback that replaced the worn one that came with the car. That was about 10 or 12 years ago. I prefer to drive with gloves (old habit) which reduces the oil from my hands getting on the wheel. The company that "restored" that wheel gave me a 90 day guarantee on the epoxy finish. The finish has held up so far but I'm afraid that it will start to show signs of wear.
You may now see where I'm headed.
A "painted" wheel will lose it's finish quickly. A wheel finished in epoxy will last longer but needs to be allowed to be cured, maybe a month or two sitting undisturbed. Placing the wheel in a heated curing environment is another option, it's quicker. Putting paint or epoxy on the wood grain part is tricky especially when you try to keep the shiny steel surfaces free, the "buttons" for example. I don't have any answers, just pointing out what I've seen and done.
Jim