When should Italy NOT take over Tunisia on its second turn in Diplomacy?
Well quickly to address the last sentence. It is actually quite common for Italy to take Tunis with an army rather than a fleet. Then with F ION and A TUN, there are options for ION-AEG, ION-EAS and the convoys TUN-ALB, TUN-GRE which aren't possible with a fleet in Tunis.

But to answer the question in the title, there are certainly occasions when Italy does not take Tunis on the second turn (and is still playing intelligently), but these are rare.

Occasionally Italy will forgo the Tunis build to try to take Greece. The other case one sees is if Austria has let Italy into Trieste in the spring, Italy is now guaranteed a build and can order ION-AEG instead of going to TUN in order to gain position in an attack (allied with Austria) against Turkey.

But I should emphasise that not taking Tunis is a minority opening, and almost always played with an expectation that Italy will be getting a build elsewhere.