Mike,
Have you checked your timing belt pulleys? It sounds like a dry idler or tensioner bearing. I thought the noise you were worried about was the wom wom noise! I asked about the "ignition" type noise previously in a PM, but I feel "ignition" may have been the wrong word.
I cant say I have ever heard a pump make that noise, or any noise to be honest. I have heard the pulley bearings make it, especially if not new and even if they are, there is still a chance to get a bad one. Also an over tightened timing belt can cause them to fail over a short period. If you spin one it should be nice and quiet and have a bit of drag. Worn/overheated ones make the lose bearing noise and seem to spin a bit easier. Also another reason I feel it is not the pump is for a better word, the noise sounds "external".
Next, if the oil pressure is really high, I would check to see if the clicking is not the pump bypassing or if you have a bypassing "thermostatic" oil cooler. Make sure it isn't bypassing causing the noise. Sounds funny, but it is quite common. In some instances you can feel the noise in the oil cooler lines. Also, if the cooler lines are backwards it may cause a clicking noise (oil pressure hitting the bypass valve from the wrong side), but you should have heard this from the start I would think. Lastly, check to make sure the oil cooler core is not clogged.
My best guess from the video is the idler or tensioner bearings. Make sure the tensioner bolt is not backing out or bending/failing.
Get your listening device! lol, and place the tip on the tensioner bolt and listen, then the idler, then the pump. This should tell you exactly where the noise is or is not from. The sump tends to amplify noises from other areas of the motor.
http://www.gtr.co.uk/forum/166480-rb26-winding-noise.html Just wanted to post up this thread so you can see how loose the timing belt may have to be on certain setups. It is a lot looser than most think. You may even need to take tension off of the tensioner.
Keep me posted
Nate