sqlite - register_converters don't trigger on Python NoneType?

import sqlite3
import numpy as np

def convert_int(x):
    print('convert_int was called with {}'.format(x))
    if x == b'None' or x == b'':
        return -1    # minus 1 as placeholder for integer nan
    return np.int64(np.float64(x))  # np.float64 needed here as int(b'4.0') throws 

sqlite3.register_converter('int', convert_int)
sqlite3.register_converter('None', convert_int)  # attempt to tigger upon None
sqlite3.register_converter('NoneType', convert_int) # attempt to tigger upon None
sqlite3.register_converter('null', convert_int) # attempt to tigger upon None

values = [(4.0,), (4,), (None,), ('',), (1.0,)]  #

conn = sqlite3.connect(":memory:", detect_types=sqlite3.PARSE_DECLTYPES)
conn.execute("create table test(p int)")
conn.executemany("insert into test(p) values (?)", values)

print(list(conn.execute("select p from test")))

yields the following output:

convert_int was called with b'4'
convert_int was called with b'4'
convert_int was called with b'1'
Out[2]: 
[(4,), (4,), (None,), (None,), (1,)]  # 

convert_int() is only called 3 times for the non-None type entries? What's the required converter I need to register in order to convert/parse the other 2 None types to some alternative value? My attempts above unfortunately don't work.