Based on those two color codes, I'd only be guessing at which one is positive. Red is positive, black is negative, is the extent of my color=polarity knowledge.
I think I just tested it first one way and then the other way and saw which one powered the GPS on before I finalized the wiring.
Are you planning to use the cigarette lighter adapter for your gps? If your GPS doesn't take 12-volt power natively, that may be the only way to go. There may be a small transformer in that adapter that is taking the 12-volts down to whatever the GPS needs. Most Garmin GPS's made for vehicles run 12-volts natively, so you can hook them right up using bare wires without trouble.
The issue with installing a cigarette lighter socket to those wires, then plugging your cigarette lighter adapter cable into it, then running that to your GPS, is that there are now several connections that can fail over time, and a typical cigarette lighter adapter isn't particularly vibration-resistant. That doesn't make it a deal-breaker, just know going into it that the connection may require some tweaking from time to time.
Which model GPS are you using?