the toroid winding, pot and transistor on the left side of the schematic make a basic joule thief circuit ... this charges the cap via a diode... once the cap charges enough to turn on (forward bias) the LED string a voltage occurs across the center LED, which has its anode connected to the 2nd transistors base and cathode connected to its emitter, this forward biases the base emitter p/n junction switching on bat1 and energzing the relay which disconnects bat2 from the joule thief. the relay will remain energized as the cap discharges slowly when its charge drops below the LED strings forward bias voltage the LEDs turn off switching off the 2nd transistor, relaxing the relay which connects bat2 to the joule thief which quickly charges the cap again.. the motor is in parallel on the bat2 side of the circuit and is powered until the relay energizes again. the circuit seems to be very very efficient... although it would appear that bat1 would drain via the relay I think what happens is the joule thief spikes bat1 each cycle which causes a charging effect to occure in the lead /acid chemistry? on the bat2 side of the circuit a joule thief is of course an efficient circuit to start with, the cap charge is used efficiently by both the leds and the relay coil and the quick pulse to the motor draws very little current as the motors coils would present a high impedance during most of the pulse. There are also claims that the spark at the contact points provide a high energy spike also???