BUG: Unable to multi column "complex" dates (file structure not yet supported)
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code Sample, a copy-pastable example

```python
from io import StringIO

import pandas as pd

data = """Date,Time,Value date,Product,ISIN,Description,FX,Change,,Balance,,Order Id
08-07-2021,04:33,07-07-2021,AAPL,,Dividend,,USD,0.97,USD,0.82,
09-07-2021,16:05,09-07-2021,Interest,LU0904784781,Buy 0.59 at 1 GBP,,,,GBP,109.53,"""

fields_en = (
    'Date',
    'Time',
    'Value date',
    'Product',
    'ISIN',
    'Description',
    'FX',
    'c_change',
    'Change',  # unknown
    'c_balance',
    'Balance',  # unknown
    'Order Id'
)


def format_datetime(x):
    return pd.to_datetime(x, format='%d-%m-%Y %H:%M')


if __name__ == '__main__':
    lines = data.splitlines(True)
    header = lines[0]
    del lines[0]
    lines = [header] + list(reversed(lines))

    df = pd.read_csv(
        StringIO(''.join(lines)), encoding='utf-8', header=0, names=fields_en,
        parse_dates={'datetime': ['Date', 'Time']},
        date_parser=format_datetime,
    )
```

#### Problem description
The above script produces following stack trace:
```
Traceback (most recent call last):
  File "/home/fugkco/tmp/beancount-degiro/venv/lib/python3.9/site-packages/pandas/io/parsers/readers.py", line 488, in _read
    return parser.read(nrows)
  File "/home/fugkco/tmp/beancount-degiro/venv/lib/python3.9/site-packages/pandas/io/parsers/readers.py", line 1047, in read
    index, columns, col_dict = self._engine.read(nrows)
  File "/home/fugkco/tmp/beancount-degiro/venv/lib/python3.9/site-packages/pandas/io/parsers/c_parser_wrapper.py", line 260, in read
    raise NotImplementedError("file structure not yet supported")
NotImplementedError: file structure not yet supported

```

What's really odd is that adding a single new line at the end of this data, seems to fix the issue, i.e.:

```
data = """Date,Time,Value date,Product,ISIN,Description,FX,Change,,Balance,,Order Id
08-07-2021,04:33,07-07-2021,AAPL,,Dividend,,USD,0.97,USD,0.82,
09-07-2021,16:05,09-07-2021,Interest,LU0904784781,Buy 0.59 at 1 GBP,,,,GBP,109.53,
"""
```

Does not produce the same exception. After investigating using a debugger, it seems that for reason I do not understand, not having the new line causes `_reader.leading_cols` to contain more than 0 columns, causing it to go into [this branch](https://github.com/pandas-dev/pandas/blob/d113a3ba559bccf285565aa934eefa2c2b5d0677/pandas/io/parsers/c_parser_wrapper.py#L258-L260). This seems odd behaviour, and it sounds to me like having a single newline or not at the end of the file shouldn't make a difference in the output.

#### Expected Output

No errors

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : f00ed8f47020034e752baf0250483053340971b0
python           : 3.9.5.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.11.0-7620-generic
Version          : #21~1624379747~21.04~3abeff8-Ubuntu SMP Wed Jun 23 02:34:03 UTC 
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_GB.UTF-8
LOCALE           : en_GB.UTF-8

pandas           : 1.3.0
numpy            : 1.21.0
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 20.3.4
setuptools       : 44.1.1
Cython           : None
pytest           : 6.2.4
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.6.3
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : 4.9.3
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None
None

</details>
