Ok, a real expression guy should be able to do this, not me, but here’s an easy solution. Put this expression on a New Null layer’s Position:
holdTime = 1.0; //time to hold each position (seconds)
minVal = [0.1*thisComp.width, 0.1*thisComp.height];
maxVal = [0.9*thisComp.width, 0.9*thisComp.height];
seed = Math.floor(time/holdTime);
seedRandom(seed,true);
random(minVal,maxVal)
That will make the Null randomly assume a position within the screen, holding for 1 sec. Change holdTime, minVal, maxVal as needed.
Now add your real layer, and parent it to the Null (Null is Parent). Add your wiggle expression to the real layer.
The Random Hold part is from Dan, here:
https://www.motionscript.com/mastering-expressions/random-1.html
When I tried to add wiggle into Dan’s expression, it jumped down and right, offscreen, so the Null was the solution for me.