The first image is that curly thing. Here's the second:

That curly thing is just a retainer maybe for the battery overflow line.

That thing just above the curly thing is the airbox drain, it's usually just dangling below the swingarm like a dingaling.

I use the curly retainer thingy to hold the crankcase puke tube coming off the bottom of the stock air box.  When I get a longer hose for the carb float bowl overflow nipple, it's going to get routed to the curly thingy too.

And SurvivingPhilly called it correctly on the starter relay.  Yours could use some clean up love.