Sure! Here’s a test case generator for the given problem statement about pluralizing Taknese nouns:

```python
import random
import string

def generate_test_case():
    # Length of the string S
    length = random.randint(1, 1000)
    
    # Generate a random string of lowercase English letters
    S = ''.join(random.choices(string.ascii_lowercase, k=length))
    
    return S

# Generate and print a test case
if __name__ == "__main__":
    test_case = generate_test_case()
    print(test_case)
```

### Explanation:
1. **Length of the String \( S \)**:
   - The length of the string is randomly chosen between 1 and 1000 (inclusive).

2. **Generating the String \( S \)**:
   - The string \( S \) is generated using `random.choices` which randomly selects characters from `string.ascii_lowercase` (which contains all lowercase English letters) up to the specified length.

3. **Returning the Test Case**:
   - The function `generate_test_case` returns the randomly generated string which adheres to the constraints of the problem.

### Example Usage:
You can run the script to generate a random test case. The output will be a random string \( S \) which can be used as input to the problem.

```python
# Example output
# Possible generated string: "apple"
```

The generated string can then be used to test the implementation of the solution to the problem of pluralizing Taknese nouns.