Can good karma, bad karma or neither good and bad karma arise or not arise from not doing?
Rephrasing Buddha, there's action that leads to good experience, action that leads to bad experience, and action that leads to dispassion and liberation.

Of course the word "karma" itself means "doing" or "action". But my teacher said, the wise sees nondoing in doing and doing in nondoing. Meaning, if you choose to drink coffee, you implicitly choose to not drink tea on that occasion and vice versa. In Mahayana terms, an "act" is empty. It is something we isolate and put a label on but in actuality it is just a point we focus on in context of everything else. When we begin seeing it like this, we begin getting closer to the Buddha's perspective.

As my Zen Master said, whenever there's choice, there's confusion. From Buddha's omniscient perspective, there's no more confusion, no action, no choice - only from the perspective of a sentient being.

Another thing that needs to be said, not all karma is personal, which makes sense if you realize that "person" is another empty point of focus. There's also group karma and other even broader kinds of karmic tendencies that don't rely on an individual action per-se. So even if you don't personally act (don't choose) you are still subject to these extrinsic tendencies. It's only when you are free from any group identification as well, is when you begin to get free from the fruits of karma.

Sorry, upon rereading this I can see it comes out a bit unclear, but this is a summary of my understanding as of the moment, based on what I have learned.