All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, may Allaah reward you greatly for your keenness in knowing the authentic Sunnah and on following it. We ask Him to bless you and us and guide us all to the right path.
You may know that there are many authentic narrations stating that gesturing with the index finger in prayer during “Tashahhud” is confirmed.
‘Abdullah Ibn ‘Umar said: “When the Prophet sat for Tashahhud, he placed his left hand on his left knee and placed his right hand on his right knee, and he formed a ring like, and he pointed with his index finger (to indicate the Oneness of Allah).” [Muslim]
Besides, ‘Abdullah Ibn az-Zubayr narrated: “When the Prophet sat for “Tashahhud”, he placed his right hand on his right thigh and his left hand on his left thigh, and pointed with his forefinger, and placed his thumb on his (middle) finger, and covered his knee with the palm of his left hand.” [Muslim]
The second narration gives some explanation to the state mentioned in the first narration.
There is another narration from Waa’il Ibn Hujr that: “He saw the Prophet when he sat in prayer, that he spread out his left foot and placed his hands on his thighs and pointed with his index finger supplicating in this way.” [An-Nasaa’i and others]
These narrations prove gesturing only with the index finger but not moving it (around).
As for the movement of the index finger, there are some narrations which prove it, while some deny it.
In the narration of Waa’il which is mentioned above, some narrators reported that he said: “I saw him (the Prophet ) moving his index finger, supplicating with it.”
As regards denying the movement of the index finger, some narrators of the narration of ‘Abdullah Ibn az-Zubayr narrated that: “He (the Prophet ) pointed with his finger while supplicating and did not move it.”
Therefore, both actions, moving the index and not moving it, are permissible.
Imaam Ibn Abdul Barr mentioned in His Book Al-Istithkaar the agreement of the scholars on pointing with the index finger during "Tashahhud" then he said: "Some scholars believe that the movement of the index finger is Sunnah while others do not. Both actions are supported by authentic narrations related from the Prophet . Therefore, both actions are permissible.”
However, the rules of ‘Usool Al- Fiqh’ and the right intellect confirm that moving the index finger is Sunnah. There is a general rule that the one who proves something is preferred to the one who denies it. Therefore, the meaning of the narration which denies the movement means that the Prophet did not keep on moving his finger in Tashahhud; so some times he did not move it. Based on this, moving the finger is a Sunnah act and not an obligatory one.
Finally, we conclude that moving the index finger sometimes and leaving the movement at other times is desirable in following the Sunnah. We say this, because it is closer to the Sunnah.
There is no specific time prescribed in the Sunnah for beginning or ending this movement of the index finger. It seems that the gesture continues from the beginning of the Tashahhud to the end of supplication.
Allah knows best.