Electron transport across a tunneling barrier is governed by intricate and diverse causes such as interface conditions, material properties, and device geometries. Here, by measuring the shot noise, we investigate electron transport in a (Ga,Mn)As/GaAs-based spin Esaki diode junction over a wide range of bias voltage. The asymmetric electronic band profile across the junction allows us to tune the types of tunneling process. By changing the bias voltage in a single device, we successively address the conventional direct tunneling, the excess current conduction through the mid-gap localized states, and the thermal excitation current conduction. These observations lead to a proper comparison of the bias dependent Fano factors. While the Fano factor is unity for the direct tunneling, it is pronouncedly reduced in the excess current region. Thus, we have succeeded in evaluating several types of conduction process with the Fano factor in a single junction.