knievel, I agree with toystory and redsox's advice, your pitman arm does appear to be
very long.
But... I feel there may be 1 other possibility you could explore here first, and that's your Toe-in adjustment.
I've found that the more Toe-in your tie rods are adjusted to, the more sensitive your karts steering will be.
Karts that have their tie rods adjusted to have no toe in, (or even more so: toed-out), tend to be much less sensitive. But this may come with the side effect of the kart wandering a bit while driving.
You may very well end up needing to drill a new hole in your pitman arm like the others suggested, but
first I'd suggest you get a tape measure out and simply measure what your current toe-settings are:
Have the kid sit in the kart while measuring, also check to make sure none of the front-end components are loose/worn and causing excessive looseness/steering-slop.
You'd just need to accurately measure from reference points (at the front and rear-center points) and across from both front tires. Sometimes its difficult to find your reference points. I recommend you first elevate the front tires off the ground and spin each tire by hand and hold a crayon up against each tire to scribe an accurate line anywhere near the center of the tread area.
Then, If you adjusted your tie rods to around a 1/4" toe-out, I think your kid would notice a big drop in his steering sensitivity level.
Then at that point, if he still desired more improvement you could consider drilling a secondary hole in your pitman arm. The tie rod mounting hole in my karts pitman arms are 2" measured center to center from the steering shaft.