Ok, now I've actually had time to check out what happens when a magnet goes past a coil (rather than all the examples I've seen, where it passes
in). I dug out my old analog multi-meter and hooked it up to the trigger wires and set the meter to the lowest scale it has, which is 10V.

The deflections were small, but very clear in the directions they were going.
The picture below shows what happens when you move a magnet towards a coil and then away--basically it induces a current going one way as it approaches the center of the coil, then the current stops as the magnet hits the center of the coil. As the magnet moves away, it induces a current going the opposite way it was going as the magnet was approaching.
The implications are that this flip-flopping is happening very fast. That waveform is happening in a fraction of a second which, of course, is what causes the sharp gradient in the rest of the circuit. Which means that the circuit is sending radiant energy to both batteries almost simultaneously. An important clue here is that the trigger signal is only seen on the load side, though.
We'll figure this thing out yet.
