The shank of the evening refers to the time between late afternoon and dusk.
If it's late in the afternoon but 4 or more hours until night time then that would be the shank of the evening as it means that the day is far from over but it's soon to be night.
The “shank” of “the shank of the evening” is a more figurative use, but, as I said, opinions vary on what it means. The phrase first appeared in print in 1828, and “shank” in this sense is defined by the Oxford English Dictionary as “The latter end or part of anything: the remainder or last part of a thing.”
That would make “shank of the evening” the time when a party is winding down, not just getting good.
But other sources define “shank of the evening” as “the main part” of the evening, which would not only agree with your understanding of the phrase, but also seem more in keeping with “shank” meaning “long, straight part of something.”
Many dictionaries, including Merriam-Webster Online, play it safe on this “shank” and offer both “the latter part of a period of time” and “the early or main part of a period of time” as definitions.