Definitely run it along the left side. The right has all the coils and a lot of other obstructions. The first time I did it without removing the tank by taking a long zip tie (or a stiff wire) and sliding it on the left side (front to back I believe) keeping it high. You'll go over the rubber tank brace that is near the middle of the tank. Now if you secure it high up on the front with a small zip tie, so that it doesn't hang down and find the best path out where the tank meets the seat you'll have it- good enough. Mine has not shown any signs of melting (over 20K miles).
Since then when I had the tank off I added a couple of zip ties to the frame but it really wasn't necessary, just looked a little neater. Here's a photo showing what's under there, including my wires for my front marker lights and the camera wire....
Sharing my experience here changing the air and fuel filter and inspecting the spark plugs. Refer to the manual for the basics, but here are things that may help, along with some very surprising discoveries I made... 1) Removing the tank There are three things to disconnect besides the bolt...