What do you mean race speed?
best laps hire kart around 40 seconds, Hamilton 39. so lets assume race speed 43 seconds, your record lap 45 seconds
Track dimensions 950 metres by 16 metres (though the racing line is a lot narrower)
That's 21 metres per second, 46 mph, 70 feet per second average speed.
Median reaction speeds for humans are about 250 milliseconds (which is why F1 cars are 'moving' if they react faster than 200 milliseconds to the lights)
human counting accuracy seems to be about 9 milliseconds
So that suggests that even under laboratory conditions the best accuracy your son could hope for would be about 6 metres, say 1/3 of the track width.
Then you are going to require your son to turn precise numbers of degrees while blindfolded. This is a nightmare situation for pilots with thousands of hours night flying, because you will encounter extreme spatial disorientation.
I suggest you sit your son in an office chair, blindfold him and spin him, then ask him to indicate simply in which direction he is a) turning and b) some idea of an accurate heading (eg: where's the door).
Your brain is keyed to respond to eyesight to keep you balanced. if you cut off eyesight the brain revert to the ear's balance system which involves fluid moving in the balance canals. The movement is not as quick or reliable as eyesight.
Quite simply, there isn't a chance you could do a "race pace + two second" lap without a supplementary directional system better than the military.
Even fully sighted, my best pace in the rain, much better conditions than a full blindfold, is probably 10 seconds a lap slower than a normal race lap.
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