With one of these old Clutch Poppers, there’s a good chance the rear tires have become quite shiny. This means they will not grip as well to a surface, therefore not travel as well/fast or spin out if going too fast on a shiny surface. There may also be some rubbish embedded in there that it would good to sand out/even out. They are made of pretty hard wearing rubber, and a light sanding can bring them back to full grip.
So take a small piece of sandpaper (120 grit or so) and just hold the rear tire and sand it lightly to rough the surface, slowly moving the tire around around doing a bit at a time until it is all even. Do the same to the other tire. Then as an optional extra you can tape a piece of sandpaper to a bench, spin up the tires to full speed and then slowly lower them onto the paper evenly a few times.
Now the thing with doing this, as well as the other two steps (axles and lube), is that if the motor is still in proper working order, the car may well go very fast if it gets revved up to max speed, and that’s where you’ll see whether you need to address any of the next maintenance steps. This one is one of the main fixes/hacks that will help it stay straight(ish) going very fast on a smooth surface, the other is weight which I’ll do another post about.