I did several hot restrikes to my Osram HWL 160W in total darkness, only to find that when the auxiliary discharge that appears as soon as I interrupting the power to the lamp, extingushes, there is a tiny discharge between the main and the auxiliary electrode, that can be seen in total darkness. This barely visible discharge seen best shortly after switch off and back on, and is less and less visible as the lamp cool down, before the auxiliary discharge reappears before the hot restrike.
Why this is happening?

There will be always some corona discharge from the sharp tips. After the electrode cool down (few seconds) and before the arctube cool down so the pressure drops, the voltage is just insufficient to cause an avalanche multiplication to form the complete spark/arc.