Chances of both blowing together are small...as VStrom3 says take 'em out and look at them (you would have to anyway!), maybe have a wiggle of wires, blocks you can see under the cowling there. Also, there is a chance (believe it or not) that the issue is related to the starter switch. This is a not-uncommon fault on Stroms (after 2005 approx).
Greywolf would probably link you here ...
http://www.stromtrooper.com/information ... blems.htmlBasically, get some electrical contact cleaner squirted in there first, see if that works. If not, you may have to dismantle the switch. Details on 'how to' are on that link.
But just to emphasise: do the simplest things first - with any luck its the big connector behind the left side tank fairing that's loose/needs a clean, especially when the bike is out all weathers.