Change Background Color DateTimePicker?

In my C# app, I'd like the components on a form to have a light red background color when entering data in that component is mandatory (and white when it's optional).  This works for all components so far, but not for the DateTimePicker --note that I want to set the background color of an 'unopened' DateTimePicker, that is, when it still looks like a combo box.  How can I do that?

Thank you in advance for your help!
StrayJayAsked:
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Éric MoreauSenior .Net ConsultantCommented:
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