> I just thought it was more time efficient to do it manually rather than spend days trying to figure out how to automate SD card pull/plug

Heres the thing. You only have to build the automation once. While it will only take you seconds at most to pull a card, you gotta sit around and be ready for the card to be pulled.

For your problem I see 2 quick things that came to minq very quickly that could do SD card pulling for you.

1) shove a level shifter in between the SD card and device under test and have a micro enable/disable the level shifter when you want to pull/unpull. ( you can even get multiplexer IC that will do the same thing as the level shifter as acting as a switch for the SD card lines, but would allow you to connect the SD card to a 2nd device (the testing pc) to allow you to write/read data from the card when its "pulled" from the DUT.

2) 3D print a jig that will insert/remove the SD card and use a cheap RC servo to handle the movement - again using a mirco to control the servo. gives a more real world test of pulling the SD card. but only gives the the ability to pull/insert. Still required manual effort if you need to read/write to the SD card

Once you have build the jig, you can reuse the jig on the next project, so while it will take some time to do/setup it could save you time later down the road.

Edit: As for the code driving the ICs or Servo, I'm presuming you already know embedded programing, but even so, a simple Arduino sketch will be able to handle it for you, fuck ton of example code already exists for it, and can be easily controlled over USB.