Passing Enum type as a parameter

"we cannot pass a Type as a function parameter" ???

Yes we can. Just look at the parameter of Enum.GetValues for example.
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Generic functions are unnecessary here. Just use Object.GetType to, um, get the type.

private Enum GetNextEnum(object currentlySelectedEnum)
{
	Type enumList = currentlySelectedEnum.GetType();

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You could have used the generic type to return a value of the correct type.

private T GetNextEnum<t>(T currentlySelectedEnum)
{
	...

	return (T)enums.GetValue(index);
}</t>