Sentence rhythm and the ear
Subject: Revision
Reading aloud is not a finishing flourish to be applied once the real work is done. It is a diagnostic, and it detects a particular class of fault that silent reading is structurally unable to catch, because silent reading lets you skim over the joins that a voice has to actually negotiate.
What it catches is breath. A sentence you cannot say without an unplanned pause has a fault in it, and the location of the pause is the location of the fault. Usually it is a subordinate clause landing between a subject and its verb, or a modifier stack that has grown one item past what a reader can hold. You do not need to name the construction. You need to notice that your voice stumbled, and then look at what it stumbled over.
Length variation is a tool, not a rule
The common advice is to vary sentence length. True, but stated that way it is unusable, because it does not say when. Length is doing a job, and the job is emphasis by contrast. A short sentence after three long ones lands like a verdict. A short sentence after four short ones is merely another short sentence, and the effect is not available.
Which means the useful version of the advice is inverted: build the long sentences deliberately so that a short one has something to land against. Writers who default to short punchy prose throughout lose the ability to punctuate, and the effect is oddly monotonous despite every individual line being brisk.
Where the verb sits
The single most reliable rhythm repair is moving the main verb earlier. A sentence that reaches its verb in the first eight or ten words gives the reader a spine to hang the rest on, and can then carry a great deal of subordinate material without collapsing. A sentence that withholds the verb makes the reader hold everything in suspension, which is a legitimate effect used once and a burden used repeatedly.
This is why the read-aloud pass so often ends with sentences that are just as long as before but easier to say. Little has been cut; the load has been redistributed.
Paragraph rhythm is the same problem
The unit above the sentence has the same property and gets far less attention. A page of paragraphs at uniform length reads as flat regardless of the sentences inside them, because the reader's eye is receiving no signal about where the weight is. A two-line paragraph following three full ones does at the page level exactly what a short sentence does at the line level.
Check this by looking at the page from far enough away that you cannot read it. The block pattern should be irregular, and the irregularities should fall at the moments that matter. If they fall at random, the shape is working against the sense; if there is no irregularity at all, no moment is being marked.
Doing the pass without wrecking the argument
Rhythm work is seductive and should be scheduled last. It is pleasant, it produces visible improvement, and it will happily consume the hours that structural revision needed. There is also a real risk of sanding a passage into euphony at the cost of precision, so keep one rule: no change made for the ear may alter what the sentence claims.
If a repair for rhythm also changes the meaning, it is not a repair. It is a new sentence, and it needs to be judged on whether the new claim is the one you meant, which is a different question and one the ear cannot answer.