I never bothered to try to figure out the circuit logic, but since we seem to have a nice group of EE's on here, I'll take a stab at it and you fellows can correct this liberal-arts-trained Pelican before the spirit of Tesla appears and gives me a shock!
When the ignition is switched on, battery voltage is present at the terminal marked +12v. This flows to the base of Q1, turning it on.
An input pulse from the Coil positive terminal enters the circuit at "1" and passes through R10 and the pair of resistors in parallel R8 and R6 to the base of Q2, turning it on, pulling its collector up to +12v. Q2 and Q3 act like a Darlington pair: when Q2 turns on, current from its collector flows to the base of Q3, turning Q3 on. When Q3 turns on, a pulse of current flows through the wire-wound resistor R11 and thermistor R12 in parallel with R5, triggering the meter movement. This current flows to ground through Q1 (conducting) and D1.
Well that was my (one) shot at it. Can somebody help me figure out the role the capacitors play? I know in a one-shot they are used for timing the pulse width but I need some help understanding how they charge and discharge to time the deflection of the meter movement.