I have a Sonnett Breakaway Puck with my 2018 Mini. The Puck is plugged into one of the Mini's TB3 ports, and the display is plugged into one of the Puck's Displayports, so the eGPU is on all the time and is used by the entire system. My desktop computers never sleep.
I have a habit of powering off all the computer related equipment when I'm done using it for the day. My Asus Station Pro and Vega 56 has a power switch, so it's easy to power it off when I shut down the Mini.