Try varying the base resistor. Exact thresholds vary between parts. I found 2N3904 to work more reliably with 4.7k.
For Rbe --> infty, breakdown is stable at Vceo. For Rbe --> 0, breakdown is stable at Vcbo. Somewhere inbetween, breakdown changes, and it is on that slope between where pulse avalanche breakdown occurs.
And yeah, it's pretty particular about voltage and current. I think mine do it around 120V (10k supply resistor?).
Apparently the breakdown proceeds as a current filament (impact ionization, avalanche cascade), which injects carriers into the base, multiplying at a much faster rate than normal. The excess conductivity discharges junction capacitance into it, causing intense local heating; this turns the filament site intrinsic, causing punch-through, i.e. the NPN junctions look like NIN, so basically, a short circuit. This maintains while the external circuit discharges, and takes about 10µs to cool down and deionize.
At low currents (just below total breakdown), the waveform looks like this:
left is a full discharge, the rest is little bits and pieces simmering near breakdown but not fully discharging.
Tim