The last ten nights of Ramadan begin from the night before the twenty first day, whether the month is complete or not

Praise
be to Allah

The last ten nights of Ramadan begin from the night before
the twenty first day, whether the month is thirty days or is twenty-nine
days. 

This is indicated by the report narrated by al-Bukhaari (813)
and Muslim (1167) from Abu Sa‘eed al-Khudri who said: The Messenger of Allah
(blessings and peace of Allah be upon him) observed i‘tikaaf during the
first ten days of Ramadan, and we observed i‘tikaaf with him. Then Jibreel
came to him and said: “What you are seeking is ahead of you.” So he observed
i‘tikaaf during the middle ten days, and we observed i‘tikaaf with him. Then
Jibreel came to him and said: “What you are seeking is ahead of you.” So the
Prophet (blessings and peace of Allah be upon him) stood up and addressed us
on the morning of the twentieth of Ramadan and said: “Whoever observed
i‘tikaaf with the Prophet (blessings and peace of Allah be upon him), let
him come back, for I was shown Laylat al-Qadr then I was caused to forget
it. Verily it is in the last ten nights, on an odd-numbered night, and I saw
myself prostrating in mud and water.” The roof of the mosque was made of
palm leaves, and we had not seen anything in the sky, but then a cloud came
and it rained, and the Prophet (blessings and peace of Allah be upon him)
led us in prayer until I saw the traces of mud and water on the forehead of
the Messenger of Allah (blessings and peace of Allah be upon him) and the
tip of his nose, in fulfilment of his dream. 

According to a report narrated by al-Bukhaari (2027), the
Messenger of Allah (blessings and peace of Allah be upon him) used to
observe i‘tikaaf during the middle ten days of Ramadan. One year he observed
i‘tikaaf until on the night of the twenty first, which was the night on the
following morning of which he would come out of his i‘tikaaf, he said:
“Whoever was observing i‘tikaaf with me, let him observe i‘tikaaf for the
last ten nights, for I was shown this night then I was caused to forget it,
and I saw myself prostrating in water and mud on the following morning. So
seek it in the last ten nights, and seek it on every odd-numbered night.” It
rained that night, and the mosque was ‘covered with palm leaves, so the
mosque leaked, and I saw with my own two eyes the Messenger of Allah
(blessings and peace of Allah be upon him) with traces of water and mud on
his forehead, on the morning of the twenty-first. 

Al-Haafiz (may Allah have mercy on him) said: 

This clearly shows that this speech was given on the morning
of the twentieth day, and the rainfall occurred on the night before the
twenty first.

End quote from Fath al-Baari (4/257) 

According to a report narrated by al-Bukhaari (2018) and also
Muslim (1167), it says: The Messenger of Allah (blessings and peace of Allah
be upon him) used to stay in the mosque (for i‘tikaaf) in Ramadaan, in the
ten days in the middle of the month, then on the evening of the twentieth,
before the twenty first, he would go back to his home, and those who had
stayed in the mosque with him also went back home.

This indicates that the last ten days begin from the night
before the twenty first. 

Hence the view of the majority of scholars – including the
four imams – is that whoever wants to observe i‘tikaaf during the last ten
nights of Ramadan should enter the mosque before sunset on the night before
the twenty-first. 

See the answer to question no. 14046. 

The odd-numbered nights of the last ten are the nights before
the twenty-first, twenty-third, twenty-fifth, twenty-seventh and
twenty-ninth. 

The night before the nineteenth is not included among the
odd-numbered nights of the last ten, regardless of whether the month is
complete or incomplete (i.e., thirty or twenty-nine days), because it is one
of the middle ten. 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

Laylat al-Qadr can only be in Ramadan, then in the last ten
nights of it, then in the odd-numbered nights of those ten, not on any
specific night among them. This is what is indicated by all the reports that
have been narrated concerning it.

End quote from Fath al-Baari (4/260) 

And Allah knows best.