Sure, let's create a test case generator based on the new problem statement. The generator will create random test cases within the given constraints.

Here's the test case generator for the problem:

```python
import random

def tcgen():
    # Generate a random N within the given constraints
    N = random.randint(1, 10**5)
    
    # Generate a random string S of length 2N with characters 'B' or 'W'
    S = ''.join(random.choice(['B', 'W']) for _ in range(2 * N))
    
    return N, S

# Example usage
N, S = tcgen()
print(N)
print(S)
```

This function `tcgen` generates a random integer `N` within the range \([1, 10^5]\) and a random string `S` of length `2N` consisting of characters 'B' and 'W'. You can use this function to produce random test cases for the problem.

Here's an example of how you can use this test case generator:

```python
# Generate a random test case
N, S = tcgen()

# Display the generated test case
print(f"Generated Test Case:")
print(f"N = {N}")
print(f"S = {S}")
```

This will print a random value of `N` and a corresponding string `S` as per the constraints. You can then use these values for testing your solution to the problem.