You can run the lead out whichever side you want (there should be a lot more than six inches of wire). When you connect the battery tender, which side is the tender located on? That would be the obvious side to locate the bike harness connector.
Everyone has their own circumstances and preferences, so there is no single answer. Personally, I prefer to have my bikes connector secured to the bike in a location where I can just pop off the weather cap and connect the tender wire without having to move the bike harness at all. Mine is secured to the metal panel between the rear of the engine and the battery compartment with heavy duty 3M exterior grade mounting tape, and it's been there for over ten years without a problem. My charger is on the wall next to where I park the bike, located where the charger harness easily reaches the bike connector. You can also use plastic tie straps to attach your bike connector to frame tubes or anywhere you desire, just make sure you locate it where it won't be damaged by heat or get pinched/crushed during operation of the bike and suspension. Once you have the connector located and secured, use ties to secure the rest of the wire harness.
Jerry