'Implied subject' independent sentences and commas

I've been reading Strunk and White's The Elements of Style, in which this rule is outlined:

Place a comma before and or but introducing an independent clause. Examples: The early records of the city have disappeared, and the story of its first years can no longer be reconstructed. The situation is perilous, but there is still one chance of escape.

Furthermore, on Wikipedia's page on the independent clause's subject (https://en.wikipedia.org/wiki/Subject_(grammar)), this example is given:

Zero (but implied) subject. 'Take out the trash!'

Thus, if 'Take out the trash' is an independent clause (with the implied subject being the person who the order is being directed to), would it be correct to write sentences like:

'Take out the trash, and move the bike!' 'Stop complaining, and do your homework.' 'Get off your horse, and drink your milk.'

I feel like the answer should be 'No' and that the correct way to write it is 'Take out the trash and move your bike!', however, I don't know why.

Punctuation is a matter of typographic and orthographic convention, not of grammar.

To apply the convention described in S&W to your sentence, you would indeed place a comma before and.

Take out the trash, and stop complaining.

stop complaining is a fully formed imperative sentence, just like take out the trash.

A more nuanced rule in the case of imperatives would be, if the second independent clause is part of a list of things to be done, then you can forego the comma:

Milk the cows and slop the hogs.

Do your homework and clean your room.

But if the second clause is a separate command, not really of a kind with the first, then use the comma:

You two pipe down, and go clean your room.

/Take out the trash and move your bike/ is an imperative and a compound sentence. The implied subject is you. There are no dependent clauses in it. The two sentences have a parallel structure and the /and/ is the linking word. Ergo, the comma rule to be placed before indepedent clauses does not apply here. However, one could - if one wanted to - put in a comma to signal emphasis or a slight pause. If that comma were in a script, the actor would read it differently than if it were not there. One has to say these things aloud to see how there might be a difference. But for me, this is not a grammatical difference.

I am not good with "rule" language, and I've been having problems with "to include a comma or not to include a comma" as well.

• You take out the trash. You wash the car. (Could be talking to two different people, or one person if your speech is really stunted)
• Take out the trash, and wash the car. (Talking to one person and the "you" is assumed in the second clause? Or can a subject never be assumed unless it's a direct imperative?) "How about you take out the trash and wash the car?" (Is the subject implied in the second clause so I should add a comma or should it be left as is?)
• Take out the trash and wash the car. (A list of two actions not in need of a serial comma unless a third action is added) Take out the trash, wash the car, and feed the lizard.