You don't have time to drill a full etiquette curriculum, and most of it wouldn't help anyway. A handful of manners genuinely change how teachers...

You don't have time to drill a full etiquette curriculum, and most of it wouldn't help anyway. A handful of manners genuinely change how teachers, grandparents, coaches, and other parents treat your child. The rest is theatre that signals which fork to use and nothing else. Here is the short list, sorted by age, with the actual words to teach.
Adults form a quick, lasting impression of a child from a small number of moments: how the child greets them, how the child responds when corrected, and how the child behaves at someone else's table. Get those right and a child reads as easy to have around, which opens doors, more invitations, more trust, more benefit of the doubt when something goes wrong. Napkin placement does not do any of that work. Skip it.
At this age you are not aiming for polish. You are building two reflexes.
Do not push handshakes, eye contact on demand, or "look at me when I'm talking to you" at this age. Small children make erratic eye contact for developmental reasons that have nothing to do with respect, and forcing it teaches anxiety, not manners.
This is the age when your child starts spending real time in other households, and other parents notice things you never will.
Around this age, adults stop grading on a curve for childishness and start comparing your kid to how a slightly older person would behave. Two manners carry most of that weight.
Almost every teenager, at some point, starts answering adults in single syllables. It isn't usually disrespect, it's self-consciousness, but adults on the receiving end read it as rudeness, and it costs a teenager more than any other lapse on this list, from job interviews to college recommendation letters to how a coach treats them.
The fix is a specific script, not a general instruction to "be more polite." Teach the two-part answer: acknowledge, then add one piece of information. Not "fine" but "good, thanks, we won that game on Saturday." Not "I don't know" but "I haven't decided yet, I'm still choosing between two things." Practice this in low-stakes moments at home so it's already a habit before it matters at a job interview or a coach's postgame comment.
The second thing worth reinforcing at this age is shaking hands or offering a proper greeting to unfamiliar adults, since this is the age it starts mattering for things like part-time jobs and college interviews. A firm handshake and a name is a two-second habit that reads as competence far out of proportion to the effort it takes.
Pick the single manner from your child's age group that they're weakest on, and rehearse the exact script with them once, out loud, before the next situation where they'll need it. Not a lecture about manners in general. One sentence, practiced once, used this week.