Yes, safety and confidence is everything. It does not matter that much at that age/stage if they learn anything at all, as long as it is an enjoyable experience. They will be ;earning simply by being there.
I always have a lead rein until the rider is ready for the lunge (as in stable in the saddle at walk and trot and able to initiate an emergency stop!). If the pony is saintly then one person is fine, but f the pony is an unknown quantity then you need 2 people. One person has the pony, the other one is in charge, has a hand on the child's knee for anything new, directs operations and is insufferably jolly (LOL only joking, it is fun so I generally am insufferably (to others) jolly as I find teaching someone new, the secret that is horse riding, absolutely jolly-making).
Usually I wold choose a nice day - an 8 yo won't be having fun if they are cold and wet.
I spend quite a while in halt just allowing them to feel what it is like up there, the slight movement of a living animal can be off-putting to some, even at halt.
Beware of adjusting the girth without warning, I have seen little ones disturbed when the saddle flap is lifted. Spend time on the stirrups, it all adds to them feeling comfortable and in control if you take it steady getting the stirrups so they are easily resting their feet. I usually have them a bt short for what people say is right for the first few times as the child can curl up a bot when worried.
I always explain what I am going to do before I do it, again, if a child is on high alert, they can be worried if the horse starts to walk and you have not told. them that we will be walking, we will walk to the gate (or wherever- but a short distance for the first movement), I want you to move your legs against the pony's side, and when we get to the gate you will tighten the rein to stop - or a longer explanation, but also with the reassurance that I am in control of the pony so you can't really get it wrong.
Once we have walked the short distance then we have a chat about how that felt, a giggle, how it felt to give instructions, and ask if they would like to go again for a half circuit of the school. Rinse and repeat.
I introduce turns etc and spend quite a while in walk, doing some, refining at halt and doing some more. At this stage I don't do much correction while they are moving as they are overwhelmed by all the new feelings to take in technical information.
Once the child is giving signals to start, stop and turn then will ask if they want to trot. I will explain that trot is like us running as opposed to walking. I ask what the difference is between walking and running, and they learn about the moment of suspension = more bounce. We do rising trot from the start, and explain that this will stop the bounce, then we practice the stand up/sit down at halt and walk.
I have a D strap as neck straps are generally either too far forwards for a little one to use and stay upright, or too loose to be of any use. Holding under the front of the saddle is also good. Again, the first trot is generally just a very short distance as they may be overwhelmed. I always hold the knee of the child whilst the leader controls the pony. The rider uses the leg to start trotting so they feel in control. A hand on the knee stops the knee flying up.
Once you have discussed and improved, go half the school a few times, discussing and improving. During these trots I do call up, down in time, as they likely won't get the time.
Once they get the up/down we will go full laps of the school.
This is generally where I would stop the lesson, on a high. It will generally have been an hour, but slowly slowly, loads of rests and chats and only trot in the last 10 minutes, with most of that time wise being at halt/walk and chat.
For the second lesson we would re-cap what we have done, and if the pony is great and the rider can not only do the up/downs but also pull up, then we would move to the lunge.
