If the Makita battery is a 6 cell lithium battery, it would be between 25.2 and 25.8 when charged, and 18v when fully discharged.
Now if you replace the 700K resistors with 100K, then the circuit starts to make sense. 700K always sounded suspicious as it is not a normal value.
U1 and Q2 the form a 12v linear regulator and it looks like C1 is to have a slow start up which will be easier on the switch, the bulb and Q2.
If it is a pre linear regulator, I am a bit surprised, as then are throwing away 50% of the battery power in heating up Q2. That is why I was think it must somehow work as a switching regulator.
And you are right Q1 has to be a PNP transistor. It is off when the battery is applied. when the battery is switched off, it turns on getting its base current through R1 to discharge C1. Change Q1 to a pnp and change the 700K resistors to 100K and you have a working circuit.
All makes sense, but very inefficient.
Richard.