Powering arduino uno from Car's reverse light?
Power the Arduino in parallel with the bulb.  Take the V+ wire running to the reverse light and the frame ground.  The frame ground is any bare metal surface of your car will be grounded, just connect a wire to your frame.  Or you can just splice the light bulbs ground wire.  When powering the circuit in parallel you do not have to worry about the amperage draw of the light.  By a barrel jack connector like this connector from spark fun you can buy these cheaper elsewhere just a 2.1mm barrel jack connector.  Connect the positive and negative respectively, and connect the 12v into the Arduino's barrel jack.  

As a side note the bulb should be getting 12V not 10V it's not a huge problem, but it is a slight issue that could later be a problem or be caused by an electrical bug.  If everything works don't scramble to fix it, but be aware it exists.