Don't sound good. Doesn't sound like rod knock to me so probably dropped valve or something in the valve train. Spray water on exhaust pipes to see if both cylinders are firing. My guess is that one ain't, the one with the dropped valve.
Try using a "probe" of some kind to isolate the region where the sound is coming from.
Since the engine is running ok, could be some kind or problem from the stator rotor, clutch, transmission, etc; anything that could generate a "click" on each roation. Possibly the beginning of an exhaust leak?
Does the sound continue when you go into gear and move under power?
Looking at the video, the oil sight glass seems empty. When mine runs the window fills up. You said you had to add a quart when you got home. It's burning oil for some reason and you ran it dry (or mostly dry), rings or valve seals maybe?
Strange? I'd run through a few things with invader!
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There are similar reports with Ninja 650R/ER-6. Tensioner sometimes needs to be removed, cleaned and worked free with WD-40... Are you sure you properly reset tensioner? What type and grade of engine oil are you using, and when was it last replaced? is your normal warmed-up idle set to 1300 rpm?