在平面直角坐标系$xOy$中,点$A(x_{1}$,$y_{1})$,$B(x_{2}$,$y_{2})$,若$x_{2}-x_{1}=y_{2}-y_{1}\neq 0$,则称点$A$与点$B$互为"对角点",例如:点$A\left(-1,3\right)$,点$B\left(2,6\right)$,因为$2-\left(-1\right)=6-3\neq 0$,所以点$A$与点$B$互为"对角点".
$(1)$若点$A$的坐标是$\left(4,-2\right)$,则在点$B_{1}(2,0)$,$B_{2}(-1,-7)$,$B_{3}(0,-6)$中,点$A$的"对角点"为点______；
$(2)$若点$A$的坐标是$\left(-2,4\right)$的"对角点"$B$在坐标轴上,求点$B$的坐标；
$(3)$若点$A$的坐标是$\left(3,-1\right)$与点$B\left(m,n\right)$互为"对角点",且点$B$在第四象限,求$m$,$n$的取值范围.