Yes

Student or Learner
"How do I find out what time somebody is appearing in court?"
Would this sentence mean the same if "is appearing" were switched to "appears"?
Yes
I think that in thess contexts every form has its own meaning and can't be switched with the other one.
1) He appears gloomy this morning. (He is appearing gloomy this morning. - WRONG)
2) He is appearing in a play this evening. (He appears in a play this evening. - WRONG)
Now I wonder why in the example with court both forms are OK.
The simple form is not wrong here.2) He is appearing in a play this evening. (He appears in a play this evening. - WRONG)
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