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Just fire the task without async/await.

private void InitMethod(ServiceControl serviceControl)
{
 if (serviceControl != null)
 {
 Task.Factory.StartNew(() => serviceControl.Execute());
 }
}

In a proper F&F task all exception handling (including a final catch, logging, notifications) is done by the task itself, so you don't need exception handling that async/await provides.

Make the method name reflect what it does. I wouldn't mind a name like FireAndForgetXyz