What we're seeing here is the impulse (i.e. a glitch) response of several slow ASC loops. In this comment, "slow" is defined by human patience, but typically means the unity gain frequencies are below the first suspension resonances, i.e. below 0.5 Hz.

Either an optic, or collection of optics gets a kick, or the the sensor signal is briefly swamped by the glitch, and sends an impulse through the ASC system (I intentionally don't specify a loop because many of the loops are cross-coupled, either in sensor or actuator, or both). Any/every linear, time-invariant, control loop has an impulse response, and these loops are no different. The response will be (roughly) the same every glich, in terms of shape and time of ring-down, because the loop filters and response is the same between them. The variety in character is just a symptom of the magnitude of impulse / glitch.

For the *very slow loops (i.e. those driven by the Alignment Dither System [ADS]), it may be that the glitch drowns out the driven error signal (the ADS lines) in the error signal (DARM / DELTAL EXTERNAL) for an "extended" period of time ("extended" in quotes because it's just "a period of time roughly equivalent to the time scale of 1 / unity gain frequency"). That means the control signal will be bogus -- thus pushing around the ASC system nonsensically, also perhaps looking like a wiggly excursion of an impulse response -- until the error signal is returned with good signal to noise ratio.

Sadly, this repetitive nature unfortunately does not mean that we are able understand the source of the glitch any better.
*BUT* these are quite slow loops, which means they take time and patience to intentionally / actively / quantitatively characterize via driven transfer function. Yet, a loop's impulse response will contain the same information as the driven transfer function. So -- maybe we can use these regular impulses to better characterize / quantify the loops (via offline study)!