Argument - 1: (denying the use with conjunctions)
If two or more clauses, grammatically complete and not joined by a conjunction, are to form a single compound sentence, the proper mark of punctuation is a semicolon.
If a conjunction is inserted, the proper mark is a comma (Rule 4)
as taken from Codified rules, Strunk & White; found via this answer
Use a semicolon to separate 2 independent clauses in a sentence, closely related, with no coordinating conjunction. Also, use a semicolon to separate items in a series where the series themselves contain commas. [source]
Argument-2: (supporting the use with conjunctions)
The semicolon between clauses suggests a connection between the sentences that is stronger than if there were a period between the two.
He is the most disagreeable person I've ever had the misfortune to meet, and I dislike his style; but I must admit that he gets the job done. [source]
The most confusing part is probably the below. It supports the use of semicolon with conjunctions with a stronger example.
Some sentences are ambiguous; however, we try hard to avoid this.
Some sentences are ambiguous however we try hard to avoid this.
The first sentence here states two separate thoughts, and points out that one is opposed to the other: "Some sentences are ambiguous" and "we try hard to avoid this".
The second sentence states that no matter how hard we try to avoid it, some sentences are ambiguous.
These two grammatically correct sentences differ only in whether we followed the semicolon-and-comma rule you mention, showing its value clearly. [source]
In summary, my question is to ask:
Which usage of semicolon is more conventional and suggested for US/UK readers?
If it helps in anyway, I'm a budding researcher in engineering. Any specific usage suites my case of technical writings if used consistently?
Just please help me with a standard answer in a way that I can cite and defend.