555 timer circuit switching automotive solenoid with PNP & NPN switching transistors
If solenoid is 12V / 0.8A = 15 Ω =Rc and Vce(sat) is rated for Ic/Ib= 50= 1.5A/30mA then Rb = (12-Vbe1-Vce2)/30mA = (12-5V)/30mA= 266 Ω @12V and 307 Ohms at 14.2V  or nearest, your choice.

But your Darlington drops 2.5V for both Vbe and Vce @1.5A so the base drive changes, if the engine has started which affects Vce(sat).  

The solenoid only gets 9.5V from 12V but 11.7V  from 14.2V.

Using a Pch FET with an RdsOn of say &lt;1% of load = 100 to 150mΩ will supply 14V to the Solenoid.







simulate this circuit &ndash; Schematic created using CircuitLab

The Diode protects the output from Excess voltage =LdI/dt, but also slows down the solenoid release due to L/R=T where R is the diode resistance ~1 ohm decay time.

Turn on Speed = T= L/DCR of the solenoid

Turn Off Damping time constant = T=L/R 
where R = 1 to 20 x DCR by choice with the diode to compromise overvoltage. V=IR =0.8 * (16+16)= 28 V or V= 0.8A x 320= 256V

Reducing the series R in the Diode increase the power dissipation and slows the response of the solenoid release as the energy must be dissipated E=1/LI^2 which can be in Watts.  Choosing series R equal to the DCR of the solenoid may be a good compromise depending on your solenoid spring and release time design specs.

Measure coil DCR with DMM and then choose 1/4W or so depending on the rep. rate of the actuator as energy is dumped in the R with low damping factor L/R.

Keep wire pairs tight for solenoid to minimize area of current loop incl diode to Vcc cap. This will reduce radiated EMI.