I recently reviewed the eGPU Pro over at 9to5Mac. I too was confused by this behavior, because the original Blackmagic eGPU powers off as soon as the Thunderbolt 3 cable is removed, or when the computer sleeps. On the eGPU Pro, the unit powers on as soon as it receives power from the power cable, regardless of whether or not the Thunderbolt 3 senses a host.
What I found is that the eGPU Pro does seem to time out, and essentially go idle after a period of inactivity. I didn't measure the time exactly, but I think it's around 10 minutes, +/- 5 minutes. At any rate, the unit does power off when it senses that it's not connected to a Thunderbolt 3 host, which means it shouldn't needlessly use up power.
You can watch my full review here:
https://9to5mac.com/2019/01/18/blackmag ... ro-review/ where I discuss this and other things about the Blackmagic eGPU Pro. I hope it's okay to link this. If not, please let me know and I will edit.
Hope this helps,
Jeff