I think your best bet would be to install a relay to control on/off of the outlet with ignition voltage.
Connect the open/closed part of the relay to your auxiliary power source, and to your outlet. Make sure you use the normally open contacts.
Then, connect the coil of the relay to any power source that comes on with ignition. It won't matter what because it will only draw a teeny tiny amount of power for the coil.
If you hook it up this way, the outlet uses the same fuse and power source as before, it just won't have power until the coil receives ignition voltage. Then you can tuck/mount the relay wherever you want.