Had a similar problem with my turn signal turned out that I had pinched 2 wires together when I put on the tank

If thats true, then wiggling the tank may expose the problem. Look at the connector under the tank. If its not seated, stuff gets weird just before it stops running.

It'd be a great time to do the head cover "door" mod. No need to ever pull the tank to get to the plug again.

Intermittant problems are usually a loose connector or a wire that has seem better days.

Since your's is a 2003, I would lean torwards a loose connector somewhere.    If the light is going out and the bike shutting down, most likely it's in the neutral circuit.  The way the circuit works,  when in neutral, two brass connectors in the tranny line up and make an electrical  "ground" to the tranny metal, and a "complete circuit" (remember your school science classes??).  But,  if the connector is loose or comes a part, you do not get the "complete circuit".  A burned out light buld shouldn't shut down the bike since it's on the other side of the sidestand diode thingy.

You will need to pull off the seat and the tank.   Then you should see a single blue wire  along the frame backbone.  There should also be a connector there.  Look there first.  Then trace the wire down the frame to see if it's pinched or cut somewhere.  It ends up down on the case by the oil level site glass.

Good Luck.