You dont need the connector even though it makes life easier.
Just flip the motherboard over and solder you power lines to the power connector solder pads.
How my 1200T was powered before I added the mediator.
Things you need to remember is while a car battery is 12v when driving the voltage goes upto around 14 - 15v due to the alternator charging the battery.
Reason why lights are brighter with the engine running and why cars have voltage regulators.
Amiga 1200 requires
+5V
+12V
-12V
GND (Car Body Earth will do)
You will need to build yourself a voltage circuit capable of turning +12v into the above voltages.
Or you could just do what i did.
Nip down to Maplins as by a 150watt Invertor for £25
Its Turn 12V DC into 240Volts AC with a AC 3 Pin Plug Socket output. Plugs into your cigar lighter or you can chop the connector off and wire it in if you desire.
150 Watts is more than enough to plug a TV and A1200 into.
Be warned it will kill your battery in no-time.
Eg If the rating of your car battery is 40 Amp Hours and your load is 10 Amps you'll get 40/10 hours use out of it. 4 hours in this case.
I would recommand an extra 100AH Leisure Battery and wiring in a split charge relay.