In the light of the broad interest of the physical-chemistry and chemical-physics communities in conical intersections and geometric phases, several studies employing the exact factorization have been conducted on prototypical situations of coupled electron-nuclear dynamics in the vicinity of conical intersections. Overall, these works concluded that in the studied cases, the time-dependent potentials do not reflect the singular behavior of the adiabatic potential energy surfaces and nonadiabatic couplings at the positions of the conical intersections. Hence, the signatures of conical intersections (seem to) disappear in the eye of the exact factorization. These studies raised the question as to whether it is possible to identify observable effects related to conical intersections without relying on the Born-Huang, or any other theoretical, representation, since physical observables are independent of the representation. This question is strictly related to a longstanding debate about the possibility of providing experimental evidence of effects directly related to geometric phases in molecules .