The function replaces every second character in the input string with the next character in alphabetical order and removes the last character if the input string length is odd.

[CODE]:
```python
def approx_function(input_string):
    output_string = ''
    for i, char in enumerate(input_string):
        if i % 2 == 0:
            output_string += char
        else:
            output_string += chr(ord(char) + 1)
    if len(input_string) % 2 != 0:
        output_string = output_string[:-1]
    return output_string
```

Let's verify this with additional inputs.

COMMAND: PYTHON(./temp/function.py "verification" "pattern" "behavior")