There’s definitely some stuff happening to the atmosphere in the scenario you’re describing, but I doubt it’s likely to be caused by particles from the debris of comet’s tail. The dust and pieces of grit are what you’re seeing as the meteor shower. The meteors you see during the Perseids will all seem to radiate from the constellation of Perseus, and even bits of dust are traveling so fast when they encounter our atmosphere that they will burn up quickly; but if they’re small enough, that burn may be so fast, and so faint that they may not be very bright. But they won’t be able to make the whole sky shimmer; meteor showers must fundamentally come from one side of the planet.
The flickering and pulsing you describe points pretty strongly to a common atmospheric effect — turbulence. Turbulence appears any time the atmosphere above you is moving around a lot, and one of the more common triggers for strong turbulence is if it’s windy down near the ground, windy higher up in the atmosphere or both. Turbulence can also show up if two regions of air which have very different temperatures meet, but wind is the most common cause.
Fundamentally, turbulence is just pockets of air which are at different densities. The flickering of the starlight comes from light bending as it comes through these pockets of air, since each one can act like a little lens. If these pockets were still, then the starlight would just be bent, and you wouldn’t notice the flickering. But the pockets of air change shape, because the wind is still blowing, and gas isn’t a static creature, and so the light will go in and out of focus. Blurring and then refocusing, the star will appear to flicker and shimmer in the sky.
So that explains the pulsing, but not the faint sky glow you’re describing. There are a couple options here; the first is that there was some light pollution from the town nearby, but you might have noticed it seemed brighter in the direction of the town than back towards the mountains. Possibly not, though — it depends on how isolated your mountains are, and how far away from town you were.
Another source of faint light can be the Milky Way – but it doesn’t sound like that was it, because the Milky Way would have been a band of brighter light going across the sky, and often looks more like high clouds and fuzziness in the sky than a glow across the whole sky.
It’s also possible that the sky shimmering with extra light is the turbulence coming back to play again — as the light from the stars in your mountains’ sky blurs in and out of focus, your eyes will pick up on the flickering brightness of the individual stars, but as the stars go out of focus, it’s possible that your eyes will interpret that as the sky itself glowing in exchange.
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