Creating a looped wiggle animation in After Effects can be achieved using expressions. Here are the steps you can follow:

1. Create a Null Object: This will control the amplitude of the wiggle¹.
2. Add a Slider Control: Go to Effect > Expression Controls > Slider Control and rename the slider control to “Amplitude”¹.
3. Apply the Wiggle Expression: Pull up the scale of your object and Option + click on the Stopwatch. Add this expression: a=thisComp.layer (“Wiggle Control”).effect (“Amplitude”) (“Slider”); w=wiggle (2,a);¹.
4. Loop the Wiggle: You can create a looping wiggle by animating between 2 different wiggle expressions². Here is an example of a looping wiggle expression:

frequency = 2;  // wiggles per second
amplitude = 40;  // amount of pixels to wiggle
secondsToLoop = 3;  // time to loop in seconds

t = time % secondsToLoop;
wiggle1 = wiggle(frequency, amplitude, 1, 0.5, t);
wiggle2 = wiggle(frequency, amplitude, 1, 0.5, t - secondsToLoop);
linear(t, 0, secondsToLoop, wiggle1, wiggle2)

This method helps you to create looped wiggle animation. Perfect for continues motion.