Are you complying with this:
- To ensure the best eGPU performance, use the Thunderbolt 3 cable that came with your eGPU or an Apple Thunderbolt 3 (USB-C) cable. Also make sure that the cable is connected directly to a Thunderbolt 3 port on your Mac, not daisy-chained through another Thunderbolt device or hub.
It seems that you are aware of this:
1. If you have a Mac mini (2018) with FileVault turned on, make sure to connect your primary display directly to Mac mini during startup. After you log in and see the macOS Desktop, you can unplug the display from Mac mini and connect it to your eGPU.
DId the eGPU work with an early macOS version or is this the first time you tried?
Go to About This Mac>Overview>Hardware, the the eGPU show up unders display and maybe Thunderbolt?