Is the use of a semicolon in the sentence 'The south sided with the King; the north with the usurper.' correct?

I have read about the use of semicolons in the Penguin Guide to Punctuation by R. L. Trask. In the book, it gives a few essential rules that must be fulfilled for a semicolon to be used correctly:

1. The two sentences must be felt to be too closely related to be separated by a full stop;
2. There is no connecting word which would require a comma, such as and or but;
3. The special conditions requiring a colon are absent.

Also, the writer stresses the fact that the two sentences on either side of the semicolon must be full sentences.

Now my question is in regard to the following sentence (I have composed it myself for a piece of writing):

The south [a region] sided with the [rightful] King; the north [another region] with the usurper [a self-proclaimed king].

The thing about my sentence is that the second part contains no verb (which is omitted to avoid repeating the verb sided). Is the sentence after the semicolon still considered a full sentence?

Thank you kindly for helping out!

If a comma were used instead of the semicolon, your sentence would arguably contain a 'comma splice'. Some traditionalists would say that that is unacceptable. However, many (I'd say more enlightened) Anglophones are prepared to accept comma splices where the sentence is reasonably short and expresses closely related truths (eg Man proposes, God disposes). This is particularly so when the second clause is contrastive (Wallraff, in the book mentioned below, suggests that a comma can be used to join independent clauses when “the whole point of two clauses is to contrast negative and affirmative assertions”.

I'd say that is true here. Barbara Wallraff in her book "Word Court" goes further than 'a comma may on occasion be acceptable', commenting on the sentence

It's not a comet, it's a meteor.:

[P]unctuating this sentence with a semicolon would be like using a C-clamp to hold a sandwich together.

(On the other hand,

Holmes found Moran, he was dead.

is best avoided.)

But using a semicolon in your example is probably even less criminal than using a C-clamp on a sandwich.

I would use a comma, not a semicolon in the example you are providing. As user Edwin Ashworth was suggesting in his comment, often it is intuitively correct to use a comma instead of a semicolon. The strict use of semicolons in such cases seems outdated to me today.