Here is a test case generator for the "Round Table of Sages" problem:

```python
import random

def tcgen():
    # Number of sages (3 ≤ N ≤ 10)
    N = random.randint(3, 10)
    
    # Array a_i (0 or 1) indicating if each sage is right-handed (0) or left-handed (1)
    a = [random.randint(0, 1) for _ in range(N)]
    
    # Array w_i (1 ≤ w_i ≤ 1000) indicating the level of frustration each sage bears
    w = [random.randint(1, 1000) for _ in range(N)]
    
    return N, a, w

# Example of generating a test case
N, a, w = tcgen()
print(N)
print(" ".join(map(str, a)))
print(" ".join(map(str, w)))
```

This code will generate random test cases that adhere to the constraints provided in the problem statement:

- `N` is randomly chosen between 3 and 10.
- `a` is an array of `N` integers, where each integer is either 0 (right-handed) or 1 (left-handed).
- `w` is an array of `N` integers, where each integer is between 1 and 1000, indicating the frustration level.

You can run this function multiple times to generate different test cases for testing your solution to the problem.