Random Motion @ Random Time

moveMin = .3; //minimum move time
moveMax = .7; //maximum move time

pauseMin = .1; // minimum pause time
pauseMax = 5.; // maximum pause time

minVal = [0.1*thisComp.width, 0.1*thisComp.height];
maxVal = [0.9*thisComp.width, 0.9*thisComp.height];

endT = 0;
j = 0;
k = 0;
while ( time >= endT){
  j += 1;
  seedRandom(j,true);
  startT = endT;
  if (j%2){
    endT += random(moveMin,moveMax);
    k++;
  }else{
    endT += random(pauseMin,pauseMax);
  }
}
if (j%2){
  seedRandom(k,true);
  endVal = random(minVal,maxVal);
  seedRandom(k-1,true);
  startVal = random(minVal,maxVal);
  ease(time,startT,endT,startVal,endVal)
}else{
  seedRandom(k,true);
  random(minVal,maxVal)
}