Q: Can you please describe the accepted usage of the semicolon? I tend to see the connection between thoughts and probably use it excessively; rather than write a separate sentence.
A: Here’s how I describe the use of the semicolon in my grammar book Woe Is I:
(1) Use a semicolon to separate clauses when there’s no connecting and or but between them and each could be a sentence in itself. Andy’s toupee flew off his head; it sailed into the distance.
(2) Use semicolons to separate items in a series when there’s already a comma in one or more of the items: Fred’s favorite things were his robe, a yellow chenille number from Barneys; his slippers; his overstuffed chair, which had once been his father’s; murder mysteries, especially those by Sue Grafton; and single-malt Scotch.
By the way, a semicolon always goes outside quotation marks. Here’s an example from Woe Is I: Frank’s favorite song was “My Way”; he recorded it several times.
The semicolon is one of the handiest – and least used – punctuation marks. I suspect that people avoid it because the semicolon intimidates them.
You obviously don’t have that problem. Quite the contrary. As you suspect, the semicolon in your second sentence is unnecessary since “rather than write a separate sentence” couldn’t be a sentence itself and isn’t an item in a series.