Once again, Ludwig Wittgenstein is on hand to help: "Whereof one cannot speak, thereof one must be silent." Tractatus Logico-Philosophicus, Proposition 7 (translated by C. K. Ogden) (1921). An alternative translation is: "What we cannot speak about we must pass over in silence."
As for the source of these intimations, I am entirely at a loss. God or gods or animula vagula blandula or imagination: you've got me. The idea of kami is attractive. Here is how Jorge Luis Borges describes them in "Shinto" (which appeared here a few months ago):
Eight million Shinto deities
travel secretly throughout the earth.
Those modest gods touch us --
touch us and move on.
Algernon Newton, "The House by the Canal" (1945)
The following poem by Norman Nicholson (1914-1987), who was a devout man, suggests one way of looking at this matter.
First on, there was nobbut God.
Genesis, I, v.1., Yorkshire Dialect Translation.
There was silence.
And God said:
'Let there be clatter.'
The wind, unclenching,
Runs its thumbs
Along dry bristles of Yorkshire Fog.
The mountain ousel
Oboes its one note.
Drips like a tap
On the tarn's tight surface-tension.
And every second nearer,
Like chain explosions
From furthest nebulae
Light-yearing across space:
The thudding of my own blood.
'It's nobbut me,'
Norman Nicholson, Sea to the West (1981).
Algernon Newton, "Canal Scene, Maida Vale" (1947)
I do not mean to slight the role of words in all of this. (How could I, given what I am doing at this instant?)
In a Word
In a word --
A green bird --
White and furred --
All heard --
Applause, applause, applause,
Something's always happening
In a word.
Norman Nicholson, The Candy-Floss Tree (1984).
Words are often our first recourse in the face of mystery. Hence: poetry.
Still, words can be unnecessary and unhelpful (harmful, actually) when it comes to the intimations of which I have been speaking. And also when it comes to poetry. This is why, as I have observed in the past, explication is the death of poetry. Although Wittgenstein had much bigger fish to fry, his remark applies perfectly to a poem: the mysterious combination of thought and feeling and sound that a good poem awakes in us is something that cannot be put into words. We must remain silent.
Algernon Newton, "The Surrey Canal, Camberwell" (1935)