If he does enjoy the actual trampolining but dislikes the waiting perhaps you could try a different class? My DD does trampolining. She is 4 and has been going for over a year. But she goes to trampolining at a proper Gymnastics club, so the trampolines are set up permanently in a corner (so no way to bounce off them!) so the others don't have to sit and watch. When they're not bouncing, they're doing a circuit of other fun activities (bouncing off a trampet, going down a big slide, playing with the little ball pool etc)... There's no way she would sit still and wait whilst the others are bouncing - so perhaps see if there is another club that does trampolining, and ask them what they expect the children to do whilst waiting?
Also, don't worry about the badges... it is not until badge 3 that it actually requires them to do anything on the trampoline. The first badge they can get is simply for knowing how to behave around the trampoline and being able to get on and off it safely! At my daughter's club, they tend to start giving badges at level 3, but if there are some children who just need the encouragement, I think they will give them the level 1 or 2 badge so they get a sense of achievement, but really you do need to do very little for a level 1.
Here's what they need to do for a level1:
"Award 1 - 6 out of 7 moves to be passed
1
Waiting turn and good behaviour around the trampoline
2
Mount and dismount to and from a central position
3
Move, or be moved, freely around the trampoline
4
Sitting and bouncing / rocking
5
Standing and bouncing / rocking
6
Lying on the back and being bounced
7
Hands and knees bouncing / rocking"
HTH