What is the role of karma in the wheel of becoming? I can't seem to find resources that tell me the role of karma within the wheel itself rather than the nature of karma. Any suggestions?
On traditional bhava-chakra images, the center of the wheel shows pig, snake, and peacock - these are the three intoxicants of Want, Hate, and Confusion (really, Reification). In the next outer layer from the center are shown human figures: half of them going up and half falling down. This is karma, good and bad. Then the next outer layer shows the six realms. And the outermost layer shows 12 Nidanas.

The relationship between layers is, the inner layers serve as causes or engines for the outer layers. So the three intoxicants, mixed like paints in various proportions, give rise to various karma classified generally in the two types, and then the fruits of karma arise as experience of one of the realms. That's from the perspective of a sentient being looking from the inside out.

From the perspective of Buddha, looking at the wheel from the outside in, the whole thing is manifestation of the spontaneous individuation (bhava) aka pratitya-samutpada, represented by 12 Nidanas.

So the role of karma within the wheel itself is to create experience of one of the six realms. Meaning, the world that you experience at any given moment is a projection of your mental/emotional state, which in its turn comes from your karma and the intoxicants. So if you make effort to not act under influence of the three intoxicants, then over time your reality will change.