Unless you have a diesel, it sounds like tappets to me. The human ear  picks up ato pick ull the surrounding noises, making a specific sound less distinguishable. A cell phone may be configured to limit background noises. A microphone typically picks up sounds closest to it. With a mic on a sound system, you would adjust the "gain" to effectively tune the distance from the mic to the sound source. Rock singers tend to set the distance very short, almost touching their lips, to get the singer's voice and not the surrounding band sounds. Generally singers' mics are set for about a foot, when the surrounding sound sources are not so close. Speakers at podiums can have the mic a couple of feet away.

As a test for yourself, try re-recording from farther away from the engine, You might have to turn off noise reduction in the phone settings.

Ah sorry about that! Updated the link for the bottom video. Agreed that the recording makes the tapping louder than it appeared but it's still louder than most videos I could find elsewhere for reference.

Both videos are the short one from the top, but it does sound like excessive valve lash to me. I'm hoping/thinking use of a cell phone to record has exaggerated the sound. In any case, that's the first place to start. Not a difficult job, just a bit tedious. 

Hi folks - have some audio from the bottom of the car and a brief one from the top (1994 SPI 1275):

• Top: https://youtube.com/shorts/2oJ7KezDL4Q?feature=share
• Bottom: https://www.youtube.com/shorts/39CkoIHqr30 (Updated Link)

Sound like a regular valve-spacing adjustment needed or bigger issue?