Thanks for the suggestions!
Unfortunately, neither of the 2 suggestions provided have helped. After some research, I'm not finding a way to change this via a command, but if I really wanted to press the issue I could open any command prompt, right-click the title bar, select defaults, go to the Terminal tab, and change the cursor colors and other properties here. Using a value of 0 for red, green, and blue would effectively make the cursor invisible on a black background.
For now, I'll simply live with it the way it is. It's not critical, just would have been nice to make the output look a little cleaner.
Note: I did see the note about using an API, but that's a bit beyond my level for the moment.
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