You probably want to repair the rear blinkers first - you know they're broken, if they're fixed, then they're probably not the issue. Take the seat off and inspect the wires to the blinkers - they run along the two black frame tubes going back.

Ready to take the tank off? Under the tank, towards the front, on the frame, there are two wiring blocks - one on the left, one on the right - these account for most wires going from the frame to the fork. You want to separate both of those blocks and reseat them to make sure they're connected.

First off, WELCOME!  

Your title also mentions the horn, but I didn't see anything about it in your post.  Is that a problem as well?

Being electrical, this CAN be a headache, but it doesn't have to be.  Go about it slowly, methodically.  I wouldn't expect the turn signal issue to be related to your headlight at all.  Honestly with such a young bike I would EXPECT it to be something simple like a loose connector.  However what we expect and reality often don't meet...  If I was having this problem I would check the electrical connector under the gas tank.  This means removing the seat - 3 bolts, then draining the gas tank, removing the 2 bolts mounting the tank to the frame, and assuming you have a stock petcock you'd do well to remove the petcock rather than fight it through the frame.  Pull that off, and lift your tank up.  You'll see a big square electrical connector.  Make sure it's snug and latched; this being loose has cause several intermittent problems in the past.

You said extended warranty; do you have to pay anything for the shop to fix it?  If you can't find the problem easily, you may consider letting them chase their tales a bit.  

I would check the left handlebar connector,under the tank.That controls headlight,turn and horn.They are known to come unplugged.

Wow. THANK YOU ALL so much for your SURPRISINGLY easy to understand replies to my wiring issue! ( hate to say it ,but I'm just not use to having guys speak to me in a language I don't have to translate somehow?....THANKFULLY we are all just BIKERS HERE!
The "tail chasing" advice for the warranty is probably the route I will be going to go AFTER I chk the connections ,BUT BEFORE I get under the gas tank.....and yes the horn is out also. I DO have the SUZUKI SERVICE MANUAL ( which I stupidly paid 150$ for) it might as well BE in Japanese! Hey anyone want a INEXPENSIVE SERVICE BOOK...TRADE A FOR A LEFT BLINKER HOUSING...LOL yeah I know there's a forum for
I WILL DEFINATLEY go to the tech section to find out what a PETCOCK  is ....right after I get up from R.O.F.A.L.M.A.O!
( cumom...I'm STILL A CHICK! It's FUNNY!)
Thanks again! Keep ya posted😘

Welcome to the forum and nice bike! Actually we technical types refer to the petcock as 'the fuel thingy under the tank'. Allow me to go all Mr. know-it-all here; the pet in petcock refers to petrol, and the second part refers to a UK term, 'stopcock' (which actually sounds kind of funny all by itself)

I have had the same problem with my headlight, horn, and turn signals.  They have been working intermittently for a long while now.   Today, with the help of a buddy who is a seasoned mechanic I should have them fix permanently.

When sitting on the bike, under the tank on the right hand side we had to cut, splice, and weather pac three wires around the bracket where they join.  Some of the connectors were corroded; although, I wouldn’t have thought we would have to fix three wires.  One was the orange, one was orange with a red stripe, and I didn’t watch him do the last.  I also had a problem in the dimmer switch by the left hand controls.  I don’t quite understand how those wires affect everything because they go to the right hand controls.  It was interesting watching him work, he followed the wiring diagram like I would read a kids book.   But it is working now.    

Best regards,

I have a '05....With bike running, I have noticed my headlight and front running lights will go out when I turn the handle bars and start to ride. If I wiggle the wiring under the right side of tank the lights will come back on.... Seems like the connection must be corroded or something like that. The wiring looks like it heads to the right grip control. Any info/ideas welcome. Ty all.