The "rattle" sounds very faint in the video and sounds more like the rattle of another sheet metal piece like a heat shield than anything engine related.
It's common for the 1ZZ-FE to have valve tic and clatter, especially at high mileage, since the valves are usually never adjusted or shimmed from stock and they don't have auto hydraulic adjustment like so many other modern engines.
I would say the best way to locate the rattle would be to have a second person look at the engine compartment with the hood open and/or under the vehicle while lying on the ground, while the engine is revved to cause the noise repeatedly until it's located.
If the exhaust manifold heat shield rusted away, it might just be another heat shield falling apart of that came partly loose and is vibrating.
One other source of engine rattle/noise on these can be the power steering pump pulley, if the mounting bolt gets a little loose, and it can just be tightened up on the engine with a ratchet and socket to quiet it back down again. If you have the tools, you might even just try tightening it down some to be sure it's good.