How to configure show when

You can put any expression into that parameter that evaluates to a boolean. Typically we use a comparison operator like <, >, =.

So I typed it out correctly, but I just need to use a different operator?

I think you'll need to provide a more comprehensive code snippet - what you have above does not look like a valid format at all.

           a!radioButtonField(
              label: "Is Jira Access Required?",
              labelPosition: "ABOVE",
              choiceLabels: {"Yes", "No"},
              choiceValues: {1, 2},
              value: ri!choiceValues,
              saveInto: ri!choiceValues,
              required: true,
              choiceLayout: "COMPACT",
              validations: {}

            ),
          
        a!columnLayout(
          contents: {
            a!dropdownField(
              label: "Which Department Requires Access?",
              labelPosition: "ABOVE",
              placeholder: "--- Select a Value ---",
              choiceLabels: {                                                   /*check AT_employeeForm when needed*/
                "Engineering",
                "Legal",
                "Accounting",
                "Corporate Ops",
                "Flight Ops",
                "In-Space R&M",
                "Safety",
                "IT",
                "Medical"
              }
          ,

              choiceValues: {                                              /*check AT_employeeForm when needed*/
                1,
                2,
                3,
                4,
                5,
                6,
                7,
                8,
                9
              },
              searchDisplay: "AUTO",
              showWhen: if(
                ri!choiceValues = true(),
                showWhen:true()
                ),
            
              required: true,
              validations: {}
            ),
    

Edited;

Rule Input used: 

These are the two components that need to interact.

When yes is selected in the radio button menu, the corresponding dropdown needs to be shown, assumedly using showWhen. It's just the actual implementation that I'm having issues with. I've looked at the documentation and reviewed the Appian video tutorials regarding Interfaces but didn't find much information in either source.

Your radio button will need to save its value somewhere - either to a Local Variable or to a Rule Input (both will work, and which one would be better depends on context that doesn't matter as much at the moment).  I notice neither of your radio button fields above saves their value anywhere (i.e. neither has a "saveInto" parameter, or a "value" parameter, meaning they will appear to not.. do anything, when you try to use them on your current interface).

After you have that resolved, you'll need to reference the saved value from the radio button in the showWhen parameter of your dropdown.

I had saved their values but had forgotten to save the changes. Adding them back in now, does the if statement I used previously seem to be configured correctly? If not, what needs to change? (besides using the ri!)

Please update your code snippet above (or less preferably, repost it in a new comment) because I still can't tell what you're trying to do given the original post's small snippet.

Updated it

You can replace the entire highlighted block with simply the following:

showWhen: ri!choiceValues = 1,

So when I do that this is the error I get: "Could not display interface. Please check definition and inputs. Interface Definition: Expression evaluation error at function a!dropdownField:", however it doesn't explain any further