If you don't need a lot of power for a real cigarette lighter, just cut off the orange (color code for BATT constant power along with RED) wire on the back of the receptacle and connect it instead to a PINK wire (the color code for ACCY/RUN/START switched power). You should be able to find PINK at the brake light switch near the pedal or going to the turn signal switch. Or use WHITE or ORANGE coming out of the ignition switch harness.
Or if you want RUN only, that's a brown wire that goes places like the HVAC control module.
You could also use one of those add-a-fuse gadgets to re-power Fuse 13 under the hood that feeds the receptacle, but since it also powers the Data Link connector used to read codes, you may not want to do that. If you don't care about the data link power, let me know and I can trace a signal that will do that. Have you seen or used those add-a-fuse gadgets? Do you have a meter to check for accessory power before tapping into things?