Thinking about it more, I have another idea.
If you attach a plane (as in the geometric concept, not the aircraft) to the base of the stick, such that it is perpendicular to the axis of the stick itself, you can intuit what is going on. Pushing the stick forward would tilt the plane at the base of the stick forward, sloping downwards to the ground. Similarly pulling back on the stick would slope it upwards away from the ground.
Honestly it doesn’t even need to be a conceptual plane, you could literally attach a model airplane to the stick oriented the same way the actual plane is, and pulling and pushing the stick would change the model’s orientation the same way that the real plane would from the same movements. Where if you pushed forward to go up, the model plane would be angled downward, contra the actual movement.
Honestly that probably is closer to the truth than anything.