Does a coordinate clause include a coordinator (/coordinating conjunction)?

Does a coordinate clause include a coordinator (/coordinating conjunction)?

For example:

"It was apple-blossom time, and the days were getting warmer."

Is "and the days were getting warmer" a coordinate clause? Or is it "the days were getting warmer" (without "and") that is a coordinate clause? Which does the coordinator "and" belong in?

https://www.thoughtco.com/coordinate-clause-grammar-1689804

In English grammar, a coordinate clause is a clause (i.e., a word group containing a subject and predicate) that is introduced by one of the coordinating conjunctions--most commonly and or but.

Practical English Usage

co-ordinate clause one of two or more main or subordinate clauses of equal 'value' that are connected. Examples: Shall I come to your place or would you like to come to mine?; It's cooler today and there's a bit o f a wind; she said that it was late and that she was tired. See also main clause, subordinate clause.

Solution 1:

The coordinator "and" is contained within (and thus part of) the second coordinate.

A simple piece of evidence for this is that a sentence division can occur between the two clauses. The two sentences might even be spoken by two different people, one adding to what the other said. And when we separate the two clauses like this, the coordinator goes with the second:

A: Ed is a good teacher. B: And his students really like him.