It is fairly mild, but works good great with adhesive residue and such.
That's part of my issue, though... I'm not sure this is adhesive residue, or whether its just the plastic/rubber breaking down...
If the entire wheel is sticky, it's not adhesive (unless the previous owner used one of those steering wheel covers and glued it in place for some bizarre reason). One would have to look at the wheel to make certain, but I would almost bet the sticky residue is from the rubber/plastic wheel itself. My Hang-On cab handle bar is also sticky in the "breaking down into goo" way sticky, not sticky with pizza grease and soda pop syrup.
Don't use GO2. It's designed to remove Latex paint and you're trying to remove sticky stuff from rubber. If the goo is the rubber itself, the GO2 would likely attack the underlying "good" rubber. Not exactly what you want. You're more than welcome to try GO2 though, I suggest a small inconspicous spot on each steering wheel and leave it alone for a few days for any problems to crop up before you go whole hog on all of them.
About the research I mentioned.
Months ago I was asked to find a way to repair and preserve our old reel to reel machines. One of the problems that cropped up (which later became moot) was the rubber wheels were either drying out and splitting apart or turning into a funky sweet smelling goo. That part of the rubber is permanently damaged, there's no recovering from it. However, you can preserve what's left if the remaining portion is viable (like your wheels).
The problem I encountered is that there's no way to tell what the rubber will do (dust or goo) so there is no a consistent method for preservation of the RtR machines. With RtR, the only universal solution is direct replacement with non-NOS rubber. A lot of potential chemicals get rejected because they damage the actual tape reels if they come into contact. Other chemicals are expensive, hazardous, illegal or all three.
Unfortunately, meet Murphy. After I did this research, everything became moot when the equipment needed to be moved out of the room it was in. During the move, most of the RtR's were shoved into boxes and stored in an empty cubical. Critical parts for the RtR machines were, "misplaced." Since it's SEP those got lost, I never bothered to try and recover the missing components. At the same time, my PC was upgraded and the HDD with the research data was externalized and stored... without a label. Again, it's SEP.
The best I can remember is
Rubber Restore but I've read nothing but nasty things about it. The other chemicals have 36 character names.
So I decided to see if I can go back and retrace some of my steps and I came across something very interesting. Since an arcade steering wheel does not have the same preservation restrictions as say... a reel to reel machine used to transfer rare audio from famous assassinations, there's a little more leeway with what can be used on the rubber.
I stress, this requires more research and thorough testing.
I've spotted some of the following products that may work for this purpose.
Armor All. Used in automobiles, go to a car parts shop for a good selection. Avoid the generic, "knock-offs," they leave some sort of weird white film after a few months. THe only problem with this is it leaves rubber kind of slick. I figure that's no problem since most of my memories of playing arcade games is with greasy pizza/french fry fingers. I've heard some people say AA reduces rubbers life expectency, but I've found no solid information to back this claim up.
303 Protectorant. Used for slingshots and similar. I've used it on slingshots, but I don't know if it's an applicable product for our purpose. It doesn't feel as slick as AA though.
Gummi-Pflege. Brother recommended. Apparently it's a product put out by BMW as a sort of equivalent to AA. From reading about the product, this appears more for dry rubber, instead of gooey rubbers.
There's SRC (Synthetic Rubber Coating) paint. I don't think it'll work for the red, but it might be useful for the true blacks. It's a rubber paint used for inflatable boats. It's intended to "bond" to the sticky rubber residue and protect them. At $100 per kit though, it might be out for us.
Maybe some samples or 1 pint cans are available?
Oddly enough, A wikipedia article cites Silicon Grease as a viable and common solution for preserving rubber. Huh.