Cell polarity in Myxococcus xanthus is crucial for the orientation and motility of individual cells. The polarity system is characterised by a dynamic spatio-temporal localisation of regulatory proteins MglA and MglB between the opposite cell poles. A minimal macroscopic model based on a reaction-diffusion PDE system is presented. Mathematical analysis of the steady states derives conditions on the reaction terms for formation of localisation patterns of the regulatory proteins under different biologically-relevant regimes (no phosphorilation, constant phosphorilation, and sporadic phosphorilation of MglA). Numerical simulations of the model system produce a stationary pattern in time (fixed polarity), periodic solutions in time (oscillating polarity) and excitable behavior (irregular polarity switching) respectively.