The function inserts the letter 'L' after the 2nd character in the input string.

[CODE]: 
```python
def insert_L(input_string):
    return input_string[:2] + 'L' + input_string[2:]
```
Let's test if this hypothesis holds with more varied inputs.

COMMAND: PYTHON(./temp/function.py "test_cases" "insertHere" "p@ssw0rd" "h#ll0")