Finding the wobbliest signal Background

I have a dataset of signals that change over time and I'd like to find the "wobbliest" of them. By "wobbliest", I mean a signal that returns consistently to zero, but does not stay at zero. This is illustrated in the figure below by the Green signal:



I do not consider the Blue signal "wobbly", since it stay at zero the whole time. Neither is the Red signal, since it seems to converge to a value.

Current Attempts

I tried getting the frequency information of each signal by doing a Fast-Fourier-Transform on each signal and setting the DC term of each signal to zero to not select for shifted signals. However, this still seemed to favour signals with large unidirectional changes in magnitude (like the Red signal) over the desired wobbly signals (like the Green signal).

Summary

How should I process my signals to find the wobbliest ones? I'm assuming I have to do some sort of operation in the frequency domain, but I don't know exactly what.
By taking the absolute value of the derivative of each signal, I was able to get the index of the wobbly signals I desired.

Here are the top 100 wobbliest signals in my wobbly dataset:


Here are the top 100 wobbliest signals in my non-wobbly dataset: