When the eGPU is re-attached, it automatically sets the external display as the primary display. If you disconnect the eGPU, your Mac defaults back to the internal graphics processors that drives the built-in display. Click Displays, then select the Arrangement tab.
Quit any open apps that you want the eGPU to accelerate on the primary display.Since apps default to the GPU associated with the primary display, this option works with a variety of apps.
If you have an external display connected to your eGPU, you can choose it as the primary display for all apps.