eGPU on an old Toshiba Satellite S55t C5222 HD Laptop
After seeing this video, I attempted the project.
I was able to connect a desktop [NVIDIA Geforce GTX 680] to a [Toshiba Satellite S55T-C5222 Laptop] which uses a [PA5195U-1BRS] battery.

I had to disconnect the WIFI module in order to connect the [PCIE M.2 cable] which connects to the [EXP GDC Beast eGPU] instead of using the supplied mini PCIE cable.
And then reattach the ethernet and USB connector.
I used a [650W Power Supply] which came with a 20+(4 pin) which I disconnected the 4 pins to connect with the 20 pin connector on the eGPU. The CPU 4-pin connector powers the eGPU. And the two GPU 6 pin connectors power the graphics card. I can use the power switch on the power supply to turn on/off the graphics card.
In the end, the NVIDIA 680 did work but I kept getting BSODs (blue screen of death). I feel like a newer graphics card would have done better but they aren’t available right now at even reasonable prices.

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Testing with old [Toshiba Satellite S55t C5222 HD] laptop…
There should be a PCI-Express connector under the WIFI adapter.