An analog echo and no reverb tank?

[Rob Strand]

I wonder if there was some sympathetic oscillation going on.

You would think that has to happen.  It's a higher order all-pass oscillator but with the feedback level just under what is required for continuous oscillation.    The ring-down at the end is like those old electronics bongos/drum projects.

Figure 5.5.1  All-pass based phase-shift oscillator:
https://sound-au.com/articles/sinewave.htm