Just as a quick demo, create a null named “Control” with a Slider Control and keep this layer at the bottom of your layer stack (below your 27 layers). Add this expression to the slider:
n = 27;
period = 1;
seg = Math.floor(time/period);
seedRandom(seg,true);
Math.floor(random(n)) + 1;
This will broadcast an integer between 1 and 27 for the other layers to use to decide whether to fade up or not. Apply this opacity expression to your 27 layers:
period = 1;
fadeTime = .25;
t = time%period;
targetLayer = thisComp.layer("Control").effect("Slider Control")("Slider");
if (targetLayer == index){
if (t < fadeTime)
ease(t,0,fadeTime,0,100)
else
ease(t,fadeTime,fadeTime*2,100,0);
}else
0
Adjust the period and fadeTime (fadeTime should be half the period, or less).