So you have confirmed that it's always the same speaker doing it (e.g. by swapping over the speaker leads), right?
This is usually an assembly-related mechanical problem, like a loose wire resonating or something. Would have to be in or near the mid-tweeter coax. Maybe even a bad tweeter or bad solder joints on the crossover. Hard to diagnose without some further disassembly.
When it's bad, it's definitely
bad (ca. 6.5-6.8 s):
View attachment 403238
vs. a clean section (7.3-7.8 s)
View attachment 403239
Your camera (phone?) seems to be normalizing audio levels quite aggressively, any chance you could turn that off? Also, a recording of the good speaker under the same conditions would be good for comparison's sake (maybe position them far enough apart).
Ultimately this seems like a case for Elac's service department.