Ok, I understand the bigger the pinion the more top speed you will get, and the same if you go smaller spur gear. And vice versa...

What I don’t understand is when to use it.

For example, if you have a modified engine that produces a lot of top end, do you match the gearing to it (bigger pinion and smaller spur). Or do you go for a smaller ratio

What about an engine that is say stock and not producing much top end. Are you gearing your car with a bigger pinion to give it more top speed down the straight?

What about an engine that has say a lot of torque and bottom end. Do you match it with a bigger first pinion?

If the power curve of the engine has a straight line then a lot of what you say works.
The problem is that the curve is not straight and a modified engine can get a wide power band or just a small peak.

And on which car? Using foam tires you do not want to start too high on the gearing ratio because later in the race you will loose speed.

Basically you only change the gearing to the type of track and not to the engine. But with that also the length of the manifold.....

Engines and gearing depends heavily on actual track testing with both the minimum and maximum foam tire diameters that will ultimately produce acceptable competitive laptimes for most of your strategic race plan...That will require lots of testing laps under different weather conditions...

Or ask the fast guy at the track who is running the same car as you. (short cut) but the philosophy is that a torque setup can accelerate with taller gearing (larger pinion/smaller spur) and an RPM setup works better with shorter gearing. (smaller pinion/larger spur) The other part of the equation is gear split between first and second gear.