```python
def tag_open(marker: str) -> str:
    if marker.startswith('<'):
        return marker[1:]
    raise ValueError("Marker must be enclosed in angle brackets.")

def tag_pair(opening: str, closing: str) -> bool:
    if opening != closing:
        return False
    try:
        open_index = marker.index('>')
        close_index = marker.rindex('>')
        if not (open_index > 0 and close_index > open_index):
            raise ValueError("Invalid angle bracket sequence.")
        return True
    except ValueError as e:
        raise ValueError(f"Invalid marker: {e}")

def main():
    # Test cases to verify the correctness of the functions
    test_cases = [
        ("<p>", "<p>"),  # Opening and closing the same node
        ("<a href='https://example.com'>", "<a href='https://example.com'>"),  # Opening and closing the same link
        ("</p>", "</p>"),  # Empty marker pair
        ("<div", "div>"),  # Invalid angle bracket pair, too few close brackets
        ("<span", ">span"),  # Invalid angle bracket pair, too many close brackets
        ("<script>", "<script>"),  # Case-insensitive comparison
    ]
    
    for opening, closing in test_cases:
        try:
            print(f"Tag Open: {tag_open(opening)}")
            print(f"Tag Pair: {tag_pair(opening, closing)}")
        except ValueError as e:
            print(e)

if __name__ == "__main__":
    main()
```

This solution implements the `tag_open` function to correctly extract the content inside angle brackets and the `tag_pair` function to determine if two opening and closing markers are the same. It includes test cases to ensure the functions behave as expected.