In mobile applications such as geomagnetic surveying, two major effects hamper the use of optically pumped magnetometers: dead zones, sensor orientations where the sensors signal amplitude drops; and heading errors, a dependence of the measured magnetic field value on the sensor orientation. We present a concept for an omnidirectional magnetometer to overcome both of these effects. The sensor uses two cesium vapor cells, interrogated by circularly-polarized amplitude-modulated laser light split into two beams propagating perpendicular to each other. This configuration is experimentally investigated using a setup wherein the laser beam and magnetic field direction can be freely adjusted relative to each other within a magnetically shielded environment. We demonstrate that a dead-zone-free magnetometer can be realized with nearly isotropic magnetic-field sensitivity. While in the current configuration we observe heading errors emerging from light shifts and shifts due to the nonlinear Zeeman effect, we introduce a straightforward approach to suppress these systematic effects in an advanced sensor realization.