The production mechanism of a 750 GeV diphoton resonance, either via gluon or photon fusion, can be probed by studying kinematic observables in the diphoton events. We perform a detector study of the two production modes of a hypothetical scalar or tensor diphoton resonance in order to characterize the features of the two scenarios. The nature of the resonance production can be determined from the jet multiplicity, the jet and diphoton rapidities, the rate of central pseudorapidity gaps, or the possible detection of forward protons from elastic photoproduction for events in the signal region. Kinematic distributions for both signals and expected irreducible diphoton background events are provided for comparison along with a study of observables useful for distinguishing the two scenarios at an integrated luminosity of 20 fb$^{-1}$. We find that decay photons from a 750 GeV scalar resonance have a preference for acceptance in the central detector barrel, while background events are more likely to give accepted photons in the detector end caps. This disfavors the interpretation of the large number of excess events found by the the Run-2 CMS diphoton search with one photon detected in the end cap as a wide spin-0 resonance signal. However, one expects more end cap photons in the case of spin-2 resonance.