Certainly! Here is a test case generator for the given problem statement:

```python
import random
import string

def tcgen():
    # Generate a random length for the strings, within the constraint
    length = random.randint(1, 2 * 10**5)
    
    # Generate random strings S and T of the chosen length with lowercase English letters
    S = ''.join(random.choices(string.ascii_lowercase, k=length))
    T = ''.join(random.choices(string.ascii_lowercase, k=length))
    
    return S, T

# Example usage
if __name__ == "__main__":
    S, T = tcgen()
    print(S)
    print(T)
```

Explanation:
- The `random.randint(1, 2 * 10**5)` function generates a random length for the strings \(S\) and \(T\) within the given constraint \(1 \leq |S| \leq 2 \times 10^5\).
- The `random.choices(string.ascii_lowercase, k=length)` function generates a random string of the given length consisting of lowercase English letters.
- The function returns two strings \(S\) and \(T\).

This test case generator will give you random test cases to test the problem "Determine if S and T can be made equal by performing the operation zero or more times."