Welcome to the Motobrick! First of all, it looks like you are new here, so a bit of an introduction is customary. A little bit about you and your bike, riding history, previous bikes, that kind of stuff.
Now, about your bike. Besides the tach, are there any other things out of the ordinary? Does the headlight and tail light work? Horn, turn signals, instrument cluster lights, etc. What happens to them when you push the starter? I can't tell from the video if the idiot lights in the cluster come on when the key is turned.
How long have you had this bike? Any previous problems? Any modifications to the bike?
I had a similar problem a couple years ago. Turned out it was the contacts inside the ignition switch. These switches do cause a similar problem to what you are seeing.
There are write ups on how to disassemble and clean the contacts in that switch.
http://www.eilenberger.net/K75S/IgnitionSwitch/http://technik.flyingbrick.de/images/6/6f/61_zuendschloss.pdf