The acid autoactivated iodate–sulfite redox reaction (Landolt reaction) exhibits bistability but no oscillatory dynamics when operated in a continuous stirred tank reactor (CSTR). However, it has been previously found experimentally that this reaction can exhibit both spatial bistability and oscillations when carried out in a one side diffusely fed spatial reactor. The precise origin of the oscillatory instability remained mainly elusive. We unambiguously show, in numerical simulations based of a kinetic model recently proposed by Csekõ et al., J. Phys. Chem., 2008, 112, 5954), that the observed oscillations are due to the faster diffusion of the proton relative to the other feed species (long range activation instability). Furthermore, our calculations account for the previous experimental observation of two different oscillatory modes. The first one is associated to localized front oscillations, as already reported in another reaction. The other one is a periodic switch between the two states of the spatial bistability and affects the system as a whole. This oscillatory mode was undocumented in the previous studies of long range activation instabilities. More complex dynamical behaviors that mix these two types of oscillations are also reported.