There seems to be a basic misconception in the question: namely, that the narrator of the poem is Eliot herself (or else, why would it be relevant whether Eliot “was an night owl”?). I feel that you wouldn’t make this mistake if it were prose: you wouldn’t read the first sentence of Moby-Dick and ask “why is Melville asking us to ‘call him Ishmael’ when his real name is Herman?” But in this respect there is no difference between prose and poetry: the narrator of a poem is just as much of a fictional character as the narrator of a novel.
Let’s have a look at the context. This poem comes from Eliot’s The Spanish Gypsy (1868), a closet drama in blank verse. In the opening scene, in a tavern in Bedmár in Andalusia during the Reconquista of the 15th century, the company are discussing the forthcoming marriage of Duke Silva to his foster-sister Fedalma. When the soldier Lopez reports that “the Duke stoops, they say, in wedding her”, the minstrel Juan fiercely defends Fedalma:
There’s a poor poet (poor, I mean, in coin)
Worships Fedalma with so true a love
That if her silken robe were changed for rags,
And she were driven out to stony wilds
Barefoot, a scorned wanderer, he would kiss
Her ragged garment’s edge, and only ask
For leave to be her slave.
George Eliot (1868). The Spanish Gypsy, pp. 29–30. Boston: Ticknor and Fields.
By “a poor poet” we understand Juan to mean himself. At this point Lopez calls for a song, and Juan sings the song quoted in the question (pp. 31–32).
In this context, it’s straightforward to interpret the song. The dark has a “joy too deep for shallow day” because it is at night that the speaker meets his lover. “Bright” and “radiant” are transferred epithets: it’s the lover who is “radiant”, meaning “bright or beaming (as with joy or love)” (OED). The description of night as “bright” creates a paradox, “an apparently absurd or self-contradictory statement, which investigation may nevertheless prove to be well-founded” (OED). The apparent contradiction creates a striking effect and requires the reader to figure out what the poet could have meant.
Note that just as we shouldn’t mistake the narrator of the song for Eliot, we shouldn’t mistake the narrator for Juan either. No doubt Juan, in the drama, has chosen this song as a way of expressing his feelings for Fedalma, but that doesn’t mean that he has actually been wooing her by night.