RX580 can only run at PCI-E x4 mode

Is this how you can tell?

Radeon RX 580:

Chipset Model: Radeon RX 580

Type: GPU

Bus: PCIe

PCIe Lane Width: x4

VRAM (Total): 8 GB

Vendor: AMD (0x1002)

Device ID: 0x67df

Revision ID: 0x00e7

Automatic Graphics Switching: Supported

gMux Version: 4.0.29 [3.2.8]

Metal: Supported, feature set OSX_GPUFamily1 v2

From my understanding, USB-C/Thunderbolt 3 doesn't have the bandwidth capability for more than PCIe x4.

At this time, the maximum bandwidth for an eGPU is 22 Gbps, per the Thunderbolt 3 specs for data (32 Gbps PCIe x4 minus 10 Gbps reserved for USB). Assuming you're connected to a 4-lane TB3 controller, and your eGPU firmware isn't old enough to have the bug that cuts the Host-To-Device bandwidth in half, you should see ~2.2 - 2.3 GBps Host-To-Device bandwidth and ~2.4-2.7 GBps Device-To-Host, depending on hardware.

Note, for those with a Macbook Pro 13" with the 4 TB3 ports, you'll want to use the left side ports to get 4-lane width.