So based solely on the fact that I have had a 4G63 for the past 13 years and seen every nut, bolt, screw and clip more than 3 times each so I'm going to take a stab in the dark here and try and help:
You changed the water pump some time back, correct?
The new water pump came with plastic fins on the fan, correct? (May not. If not, noise is louder)
The noise in the clip above increases with throttle but almost goes away sometimes (motorways etc), correct?
I'd say that your water pump is on its way out and the fan shaft has play in it. The fins of the fan actually sit inside the block (think room fan, and block is the blade guard) and when it's under load (pump is driven by cam belt) it's being pulled off centre slightly and the edge of fan fins are collecting the block and making that noise.
Take the top and middle cam cover off, locate pump (back edge, bout halfway down block) grab the pulley and wiggle. If it moves that's your problem. If it don't move, you just wasted 10 mins reading this and 30 mins pulling off some covers.
Now, if it's your lifters or anything that is touched by oil really then go buy some 'Promar MLB8' because this stuff is AMAZING!!! 92 Lancer GSR with lifter noise so loud you could not talk to someone by car, add 70Ml MLB8 with oil change and wait 2mins......... GONE, not reduced, GONE! and till next service too. That sh1t is simply incredible.
On a side note, is it an Auto? Cause if it sounds more like an exhaust leak than a ticking and the pitch of noise changes when you Change from P to D and D to N etc with park being quietest then it may well be your 'Throw Out Bearing' which is the bearing that engages the clutch plate from the gearbox.
Try this - disregard all thoughts about what the noise is, start the car, close your eyes and ask yourself "does it sound like a bearing that's got no grease in it that is spinning hard out." Hmmmm, Does it?
Good Luck Mate