There is no direct solution for an empty DateTimePicker . The only way to reset DateTimePicker is to set CustomFormat and then set empty space as value.
dateTimePicker1.Format = DateTimePickerFormat.Custom; dateTimePicker1.CustomFormat = " ";
Even if you do, the value will be cleared in the control, but if you access the value of the property of the control in the code, it will return the current time. Therefore, your condition will always be false.
//This is always false dateInsert.Value.ToString() = string.Empty
Decision
Instead of using Value use Text in the condition.
if(dateInsert.Text = " ")
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