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You must check punching for all load cases. If (1.2Dead+1Live+1EQ) giving you more forces you should check punching on that. But also remember that, you should check both axial plus moment. So may be you are getting more M in in this combination but axial force is less. So you should check which load combination is giving you more shear stress. You should all load combinations whether it is EQ or gravity or W anything.

In my understanding these are NOT 2 different methods; This is just a differentiation; There are two torsions; 1. Compatibility torsion (where redistribution of moments take place) like slab on beams 2. Equilibrium torsion (where there is no path available for redistribution of moments, like a cantilever slab resting on a beam) These are not two different methods of analysis in ACI or ETABS. This is just to distinguish the cases. That is why it does not matter in ETABS because in ETABS loads will follow the paths that is available. So does not matter if it is case 1 or 2, apply J modifiers but watch for slab moments. Also make sure your detailing handles all these issues. For example if the beam is torsionally too stiff as compared to slab, it will take more moment as compared to slab, and if you are applying less J modifier to beam then make sure the detailing also follows the same approach. (try to increase bottom reinforcement of slab).