Background: The predominant mass-asymmetric fission of actinide nuclides occurs mainly through the so-called standard I and standard II modes. Though understood to be caused by shape-dependent shell structures encountered between the fission barrier deformation and scission, the most relevant shell gaps are still not firmly established. The standard I mode had been associated with the spherical doubly magic $^{132}\mathrm{Sn}$, and thus the $Z=50$ proton shell, but recently it has been proposed that standard I and standard II are associated with quadrupole and octupole deformed gaps at $Z=52$ and 56, respectively.Purpose: We investigate how the relative probabilities of the standard I and standard II modes vary with excitation energy near threshold, probing where the two modes bifurcate.Methods: The Australian National University Heavy Ion Accelerator Facility and CUBE fission spectrometer have been used to measure fission mass distributions for the $p{+}^{232}\text{Th}$ reaction (forming $^{233}\mathrm{Pa}$) at closely spaced bombarding energy intervals from 6.5 to 28 MeV.Results: A model-independent analysis of the energy dependence of the shape of the mass-asymmetric peak shows a strong dependence of the standard I and standard II relative probability on excitation energy near threshold.Conclusions: The results are consistent with the standard II mode having a lower fission barrier than standard I in $^{233}\mathrm{Pa}$, with the latter increasing continually in relative probability above its barrier energy. It is concluded that multichance fission, in particular last chance fission, plays a strong role in determining the observed energy dependence of all fission modes.