Extension for CCFL tubes
Just to make it clear: you're right that you should extend the 12 V side, not the 680 V. Not only should  the bulb side wiring be short, it must also have it's insulation in good shape.

680 V @ 5 mA is about 3.4 W
By the 12 V side, that's around 360 mA at a low 80% efficiency for the inverter.
Low enough power that you shouldn't worry much about your method for extending the existing 12 V wiring.

For a very clean setup, you could buy Molex pins that can be crimped with a pair of pliers and 20 AWG wire to run from the PSU to the inverter without splicing anything. That's what I'd do.

If you want it cheaper, you could safely get away with cutting the existing wiring and soldering or using a butt connector to extend the additional 7½ meters.