The highly successful Dirac equation predicts peculiar phenomena such as Klein tunnelling and Zitterbewegung (ZB) of electrons. From its conception by Erwin Schrödinger, ZB has been considered key in understanding relativistic quantum mechanics. However, observing the ZB of electrons has proved difficult, and instead various emulations of the phenomenon have been proposed producing several successes. Concerning charge transport in semiconductors and graphene, expectations were high but little has been reported. Here, we report a surprisingly large ZB effect on charge transport in a semiconductor nanostructure playing "flat pinball". The setup is a narrow strip of InAs two-dimensional electron gas with strong Rashba spin-orbit coupling. Six quantum point contacts act as pinball pockets. In transiting between two contacts, ZB appears as a large reproducible conductance fluctuation that depends on the in-plane magnetic field. Numerical simulations successfully reproduced our experimental observations confirming that ZB causes this conductance fluctuation.