We study the conductance $g$ of an electron interferometer formed in a two dimensional electron gas between the charged tip of a scanning gate microscope and a nanostructured quantum contact. If the contact transmission exhibits successive resonances, we show that the images giving $g$ as a function of the tip position can exhibit novel interference rings in addition to Fabry-Pérot interference fringes spaced by half the Fermi wavelength. This is due to a beating effect between the contribution of two successive transmission peaks to $g$ and can be observed when the contact is opened between the peaks at a temperature of the order of the inter-peak energy spacing. We analytically study two contacts exhibiting the required double-peak structure: (i) The first one is made of a single quantum impurity with a parallel magnetic field, the spin degenerate Breit-Wigner resonance of its transmission being split by Zeeman effect; (ii) The second one is made of an inversion-symmetric double dot setup, where the pseudo-spin degeneracy is broken by the inter-dot coupling. Numerical studies of a quantum point contact with quantized conductance plateaus confirm that similar beating phenomena can be seen near a spin-split channel opening, when a parallel magnetic field is applied.