Great, here is a variation on the expression to lock one of the axis, as well as control the time interval the position changes.
To precisely control where the axis position is, I used (+b) I am sure some guru on here will figure out a much better way, but I like it:-)
Thanks to Dan!
holdTime = .5; //time to hold each position (seconds)
seed = Math.floor(time/holdTime);
seedRandom(seed,true);
numberOfXPositions = 1;
numberOfYPositions = 30;
a = 10; //fixed number value
b = 512; //fixed number value
x = Math.floor(random(numberOfXPositions))+b;
y = Math.floor(random(numberOfYPositions))*a;
[x,y]