I'd prefer it be renamed to Agility in this context. Though I'd like to change things around a bit - the following is not related to your context of Jump, but to something that I just cooked up in reply to it.
It reminds me of Parkour and rock climbing in a way. Vertical Jumping, even up a cliff, is a matter of total-body strength, agility, coordination, flexibility, and endurance. Same with Horizontal Jumping, though this is much closer to Parkour than it is to rock climbing. Even Move is equivalent to stride length, movement speed, coordination, strength, and endurance.
My point is that both "physical" stats - Speed, and PA - should be used to calculate Move and Jump, and perhaps HP can serve as endurance, so it will modify them.
Move = ((PA + SP) / 2 ) * (Current HP / Max HP)
Divisor depends on patch (average PA and SP), obviously. It would keep in line with Physical classes having better move and Jump. And I'd like to limit the amount of Move you lose when your HP drops, but I don't have the math to represent it. Like, if you're HP is at 100%, then you get the normal Move. If your HP is at 50%, then you get 75% of the normal Move. And if your HP is at 1% or below, then you get 50% of the normal Move. This, along with the modifications of Jump listed below, would make Razele's Flee Movement ability incredibly useful. By which I mean it will save your ass when you're in a bind.
Vertical Jumping = Move * (7 / 8)
Vertical Jumping (the visible Jump stat in Vanilla, though the vanilla stat isn't derived from other stats) would be invisible in this case, unless someone does so GUI hacking. I'd love it to be visible, and for it to be recalculated as it you change your equipment and job class in the formation menu. And I'd want it named as Vertical Jump, or just an up arrow and the word Jump.
Horizontal Jumping = calculated Vertical Jumping / 2
This is the vanilla formula for Horizontal Jumping by the way. And I'd like it to follow the same rules as Vertical Jumping when it comes to recalculation in the Formation menu, and I'd like a sideways arrow with the word Jump.
There are a lot of other things I'd like visible in FFT. The "Stepping Stone" attribute is one of them.
And one other thing: if I change it like this, then how would equipment an abilities that modify Move and Jump stats fit into this? It's probably easier to clone FFT than it would be to rearrange FFT to fit this in.
I should probably change Class Physical Evasion to be derived from PA and SP somehow, too.