To be honest I think you should run a separate connection for your inverter because if you draw more than 5A (60W) from your lighter socket the car wiring will get quite warm and at full load of 16A it will melt. The Cig Lighter wiring is only rate for short term use. I do alot of Camping out in the Ozzy bush and use inverters and have dedicated cabling and batteries etc So that said that will leave your Cig lighter for your GPS.
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