I have read thousands of emails from account managers over the years, and I can usually tell in the first ten seconds whether one will get a same day reply or sit untouched until someone follows up on Slack. The difference almost never comes down to politeness or length. It comes down to whether the reader knows exactly what you need from them and by when.
The buried ask
Most slow emails have the actual request hiding in paragraph three, after two paragraphs of context nobody asked for. Busy people skim. If the ask is not visible in the first two sentences, it competes with everything else in their inbox and usually loses.
Put the ask first: "I need your sign off on the renewal quote below by Thursday." Then give context, not the other way around.
One topic, one email
The second most common mistake is stacking three separate asks into a single message because it felt efficient to send once. It is not efficient for the reader. They can act on one clear thing immediately. Three things in one thread usually means the easy one gets answered and the other two get lost.
If a message has more than one ask, split it into more than one email, or number them so plainly that nobody has to reread the message to find what is still open.
Say the deadline out loud
Vague urgency reads as no urgency. "Whenever you get a chance" is an invitation to reply next week. If something is time sensitive, name the date and the reason: "I need this by Wednesday so I can get it in front of legal before their cutoff."
The best account managers I have worked with treat every email like it is competing for five seconds of attention, because it is. Say what you need, say it first, and say by when. Everything else is context the reader can get to after they have already said yes.