OK, No Problem
Yes run a new 10 gage wire with a ring terminal from your battery thru a 15A fuse to the back side of the lighter. There is a hole with rubber grommet just under the Brake Booster to snake the wire thru the fire wall. I don't know what kind of terminal is attached to the OEM lighter, but its probably a spade type connector.
The lighter will have a ground wire going to a terminal under the center console (is my guess) that's were the main ground is for the dash stuff.
You can reuse it if it has enough slack or run a new ground wire from the lighter through a switch on the dash. It can be a toggle type a or a fancy type that mounts in an empty switch plate hole.
Ring Terminal
View attachment 1858963
inline fuse holder
Toggle switch and wire
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If you think you might want to have more electric things in the future, run a multi fuse buss, like from Blue Sea.
View attachment 1858974
This is the one I chose, its mounted with sst screws to my fire wall.
View attachment 1858965