What determines the pathway of a neurological signal?
Short answer
Neuronal signals neither choose where to go, nor do they carry routing flags of some sort to guide them. Instead, neuronal signals are guided by the hard wiring of the nervous system.

Background
Neuronal signals (action potentials) basically follow a one-way path. When they encounter a cross roads, action potentials are simply propagated to all of those alternatives. External effects of neurons, hormones or drugs may alter these signals, for example by inhibiting action potential formation or propagation. 

To take the example of the auditory system (Fig. 1):


Fig. 1. Auditory system. Source: New York University.

One can readily see that the signal from the hair cells are routed into the auditory nerve to the cochlear nucleus, from there to the colliculi in the brain stem and further up to the auditory cortex via the medial geniculate. Basically this is a one-way, straightforward route.

There is complexity in the system, however. For example, the fibers of the auditory nerve bifurcate on entering the cochlear nucleus and make synapses on a number of morphologically different types of neuron. Each of the latter sends its axon out of the cochlear nucleus with a distinctive projection pattern that gives rise to further divergence. Specifically, some cochlear nucleus neurons project directly to the inferior colliculus, whereas others project to various divisions of the superior olivary complex and nuclei of the lateral lemniscus, which in turn project to the inferior colliculus (Irvine, 1992). 

But even in this complexity the divergence is basically generated by simple bifurcations. An action potential reaching such a junction by default simply gives rise to two parallel signals; there is no choice involved. Regulation is due to other neurons targeting these pathways. 

Reference
- Irvine, The Mammalian Auditory Pathway: Neurophysiology Springer Handbook of Auditory Research (1992).