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The scarce optical variability studies in spectrally classified Type 2 active galactic nuclei (AGNs) have led to the discovery of anomalous objects that are incompatible with the simplest unified models (UM). This paper focuses on the exploration of different variability features that allows to separate between obscured, Type 2 AGNs, and the variable, unobscured Type 1s. We analyse systematically the Zwicky Transient Facility, 2.5 years long light curves of ~ 15000 AGNs from the Sloan Digital Sky Survey Data Release 16, which are generally considered Type 2s due to the absence of strong broad emission lines (BELs). Consistently with the expectations from the UM, the variability features are distributed differently for distinct populations, with spectrally classified weak Type 1s showing 1 order of magnitude larger variances than the Type 2s. We find that the parameters given by the damped random walk model leads to broader Hα equivalent width for objects with τ_g > 16 d and long term structure function SF{\infty},g> 0.07 mag. By limiting the variability features, we find that ~ 11 per cent of Type 2 sources show evidence for optical variations. A detailed spectral analysis of the most variable sources (~1 per cent of the Type 2 sample) leads to the discovery of misclassified Type 1s with weak BELs and changing-state candidates. This work presents one of the largest systematic investigations of Type 2 AGN optical variability to date, in preparation for future large photometric surveys.