Why neutral Italy removes the historical Afrika Korps

Why would the Afrika Korps exist in a scenario where Italy stayed neutral?

It would lose its historical reason to deploy in support of Italy's North African campaign; the proposed Italian civil war keeps Italy out of that conflict.

The Afrika Korps was sent to support Italy's North African campaign, so the proposed neutral-Italy scenario removes the reason for that deployment. A qualification distinguishes neutrality toward the Axis war from an independent Italian war against Greece. This particular scenario instead keeps Italy occupied by civil war and out of both campaigns. The imagined trigger is a clash between Mussolini and the king over an equal marshal's rank. In Clarke's counterfactual, refusal by the king prompts Mussolini to attempt a usurpation, while the army's loyalty to the monarchy turns the crisis into civil war.