if you dont already have it, google Yamaha V star 650 factory service manual.
You can find it as a free PDF download
look at the exploded drawings for the front axle, make sure you are not missing a spacer or washer, or someone didnt put it on the wrong side.
There should be nothing to center, adjust, wiggle or settle when you put the front wheel on the bike. Put the axle bolt thru with all the right parts and torque it down, then torque down the lock bolt.
If you can move things around, a bearing is shot or parts are missing or in the wrong place, or worse yet your fork is bent or loose!
is interesting about the CEL light - there is no sensor on the front wheel, its a mechanical gear/wheel that spins the mechanical cable, which begs the question: If its not connected and the cable is not turning while you are riding, how could the ECM possibly know you are riding, and that the bike is suppose to be moving?!