The timing chain & related parts can make all sorts of funky noises when they are going out. I can't say for sure what might be the culprit from those sound clips, but I would not put the timing assembly out of the realm of possibility. Honestly, the only way to be sure is to pull the upper & lower timing case covers & check. That can be done in about 2 hours.
You need to:
- Drain coolant (dispose of it responsibly, not in the gutter)
- Remove engine fan & shroud
- Remove thermostat housing, water pump pulley (loosen w/ belt on, then release the tension at the alternator) & water pump
- Disconnect & remove cam + crank position sensors
- Remove PS & AC belts
- Remove crank pulley & harmonic damper
- Remove 22mm bolt on crank (usually needs 200+ ft-lbs*)
- Remove valve cover
-Remove upper & lower timing case covers.
- Inspect timing assembly components. Take pics & post them here, with close-ups of each component.
- Reassemble everything in the reverse order. You will need all new paper gaskets, and they should be coated with a non-curing sealant (both sides) that is rated for use in auto environments with coolant and oil at high temperature. You should also replace the rubber profile gasket & seal it along the perimeter & especially at the ends with high temp, oil resistant silicone RTV (Permatex Ultra Black is recommended).
- Before tightening the bolts on the upper cover, get some spare M6 (20-30mm) screws & bolt the valve cover (no rubber gasket) onto it so it pushes the upper cover flush with the head. The stock valve cover bolts don't work for this because of their shoulder. When held flush you can tighten the upper cover's fasteners.
This is a lot of work. I can't guarantee that the noise is timing related. The crappy thing is that these motors are all old enough that that stuff is probably going out. Oil changes & fresh tensioner pistons help a lot, but eventually it all needs a tear-down. Does the car run any differently when warming up & making this noise? Does your intake show a lot of soot or other carbon build-up? The noise almost sounds like a leaky valve, but I would think it would be noisy all the time.
Have you looked for vacuum leaks? Is the idle uneven & stumbling? Do you get check engine lights when you floor the car for more than a few seconds? It could be a big leak that closes up once things warm up & expand. Heck, maybe it is some sort of exhaust leak.
* Remove the air filter box. Place a block of wood over where it was. Get a 18" breaker bar on the bolt & rest the bar on the wood. Use the car's starter to break it loose (usually takes 2-3 tries). Some people leave the bar 6-12" above the wood so the bar smacks into it to break the bolt loose. I don't like that, but it might work better. Do NOT remove this unless you are sure you can get it back on with at least 200 ft-lbs, the spec is 240 ft-lbs. You will need some way of locking the crank...you might be able to put the car in 5th gear & press on the brakes. The clutch usually slips though. This step should only be done if you are sure you can put the bolt back tight enough! I machined a steel plate that bolts to the pulley hub & rests on the frame.