After studying the circuit, I'm fairly certain the way it works is that when a particular bulb fires, the other bulbs that are capacitively coupled to it will extinguish. Neon bulbs have built-in hysteresis (firing voltage is higher than sustaining voltage), which means that circuits can be constructed that self-oscillate.
So, back to debugging, if the capacitors are leaky I think it could prevent oscillation. Also, I'm not sure what resistors R2, R5, R8, R11, R14, and R17 do, so you may want to snip them off temporarily for debug. I dont think the transistor circuit will cause any interference.