I'd start with the dash. You are probably gutting to a level that it should be removed anyway for A/C/heater work. It's the more complicated area of the car. Then rear harness and front/engine harnes last probably. You can do testing with a battery charger as long as it's fused and you have a filter capasitor across the output. Chargers are very "dirty" 12v supplies. To clean it up when testing radios or other electronic accessories (alarms, power windows/locks) you can use a 10,000mFd electrolytic @50v. Hook it up plus to plus,minus to minus.
Just keep in mind access and order of reassembly... you don't want to 'paint yourself into a corner'.
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