Why is the Thomson effect usually neglected when analyzing thermoelectric generators?

In the analysis of thermoelectric power generators, the Thomson effect is generally neglected because it is comparatively small in magnitude.1

While the Thomson effect describes the absorption or evolution of heat along a material rod subjected to a temperature gradient and an electric current, practical device analysis is adequately described using the Seebeck coefficient ($\alpha$) as the primary thermoelectric parameter. Because the Thomson effect contributes minimally to the overall thermal and electrical performance compared to factors like Seebeck-driven voltage, thermal conduction, and ohmic heating, it is typically omitted to simplify the modeling of the device's operation.12