"Should you ever use private on fields and methods in C#?"
Yes, but, it depends in your code logic.
Long Boring Extended Answer:
I suggest, always specify vissibility for members.
I think It is a good approach to declare members, by default, as "private".
In real world, I use "protected", instead.
Sooner, or later, that hidden member, could be used by a subclass.
Sometimes, a good question, can be better answered, by asking the opposite question.
The opposite question, to your question, could be something like:
"Should I use always public access modifier on fields & methods in C#"
In other programming languages you can "promote" protected to public,
depending on your design.
I use a lot of (visual) control deep hierarchy libraries, where,
some members (properties, methos) are required.
Sometimes, is better to have them public, sometimes don't.