Yes that's it, just peel back the rubbers on the two posts and bridge them (only a second just to see if the starter motor turns, ignition on when you try, use a good insulated screwdriver and try not to weld it to the posts, )

 

Ok, jammed a screwdriver in there while wearing a silicone oven mitt. The bike turns over and starts. So it's something with the kill switch or starter button?

 

No , you need a new starter solenoid like this one
New Starter RELAY SOLENOID SOLONOID HONDA CBR600 RR RR3 / RR4 03-04

 

Ok, will get one and swap it out. In the mean time, would it be worthwhile checking the connections in the right handlebar to the killswitch/starter button?

 

You can for piece of mind , but if your going to clean in side ,use WD40 Electrical or Dielectric grease ,and not the normal WD40, I see your in USA and your bike is 2007, so one of thesehttp://www.ebay.co.uk/itm/Starter-So...MAAOSwaNBUhzd9