Videos are really difficult to get a feeling for how the noise conveys in real life. Based on what's in the video, it sounds more like a noisy lifter or lifters than nailing. Nailing is usually a very sharp "rap" noise, literally like someone hitting a hammer on an anvil. The noise in the video sounds more like something that's mechanically sloppy. I had a collapsed lifter on Cyl 6 on my SDL that made an alarming amount of noise at idle when the engine was hot. The 606 uses a similar lifter design, but has 24 of them instead of 12. Noisy lifters are common on the 603, not sure how common it is on a 606.

I'd be concerned with the amount of air in the fuel lines though. Any air is bad, but when you rev the engine in your first link, there's an alarming amount of foam going through your plastic fuel lines. Believe it or not, that could be your only problem. Air can and will cause nailing and injector noise.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]