We report magnetic quantum oscillations measured using torque magnetisation in the Kondo insulator YbB12 and discuss the potential origin of the underlying Fermi surface. Observed quantum oscillations as well as complementary quantities such as a finite linear specific heat capacity in YbB12 exhibit similarities with the Kondo insulator SmB6, yet also crucial differences. Small heavy Fermi sections are observed in YbB12 with similarities to the neighbouring heavy fermion semimetallic Fermi surface, in contrast to large light Fermi surface sections in SmB6 which are more similar to the conduction electron Fermi surface. A rich spectrum of theoretical models is suggested to explain the origin across different Kondo insulating families of a bulk Fermi surface potentially from novel itinerant quasiparticles that couple to magnetic fields, yet do not couple to weak DC electric fields.