I will try to give a clear answer. In the last chapter of Masechet Nidda we have a Mishna, two Beraytot and a Gemara which address the issue.
Let us take the case of a woman who is Nidda (to simplify She has menses). The verse establishad that sshe is unclean for 7 days. At evening, after the end of the 7st day, she already can go to mikve and become clean.
After "the 7 days of nidda" start "11 days of ziva". In ziva days, an other kind of uncleaness may appear. (Ziva is an other kind of uncleanness which characterises extra menstrual bleeding.)
The period of nidda days is a period of time in which potentially bleeding is normally, may be expected.
But the bleeding may interrupted before. When we are sure that the menstruation is finished, there is no a great risk for intermenstrual bleeding, even if the nidda days are not yet completed (how true is this is discussed by Tanaym).
Case: A woman had a menstruation which ended, and she toveled leil shmini (biblical hilchot nidda which don't need sfirat 7 nekiim). After a couple of days she had a new uterine hemorrhage. We have to know for several reasons, the status of the days in the interval between the end of the first bleeding and the starting of the second bleeding.
To do this we use an halachic principle called chazaka. When we are sure that the first bleeding interrupted we say that she is bechezkat mesuleket damim, the hemorrhage is remote.
We found four opinions, three in Mishna and a last in Berayta, concerning how to ensure tha she is not bleeding further by short intervals.
- Tana Kama,
- Rabbi Yehuda
- and Rabanan.
- A fourth opinion which does not appear in Mishna is cited in Berayta, which Rashba ruled in Halacha and called it "ziknute Derabbi". Mishna and Gemara are in folio 68ab of Masechet Nidda.
1.Tana Kama stated that if in the 7th morning she noticed that the bleeding has stopped, she is Bechezkat Tahara until the second bleeding.
2.Rabbi Yehuda said that the arrest of bleeding cannot be authentificated until the 7th Afternoon.
3.Rabanan said that the second day at morning is still late enough to authentify the stopping of bleeding.
4.The fourth opinion ( ziknute deRabbi ) ruled this even for the first morning.
What is the difference between the first day and the second day for the Rabbanan of the Mishna?
The first day is just a day in which there was undoubtedly begining. In such a day we cannot state rule a Chazaka of Mesuleket Damim before a further observation that the hemorrhage has stopped. Such a day is called in Gemara a day in which her "source" was opened.
I've seen that the reason for a moch dachuk is to make sure there was no further blood flow from the time when the hefsek tahara bedika was done until nightfall.
--> Yes a Tana in Berayta, this view is a further layer in the stringent reasoning of Rabbi Yehuda.
Rabbi Yehuda is the most stringent. In Berayta, his oponents. Said him that followind his stringent reasoning she needs to be watching without interruption until the nightfall.
A technical possibility of continuous watching is the Moch Dachuk.
But if there was blood flow, then it will show up on the next day's regular bedika.
--> No, "אין כותלי בית הרחם מעמידים את הדם" (The walls of the womb do not hold blood back.) (the conclusion from halachic point of view, from Nidda 3a).
Yes, we won't know exactly when the flow started (i.e. before or after nightfall)
If you are speaking for Yikar hadin of 3 Yeme Ziva, may be true, for an hefsek after the 3rd day, but for an hefesk in the 2nd day, no nafka mina, to tvila she need to wait until leil 8. If you ask for kviut Veset, I don't know (perhaps a big stringency). If you ask for breaking the 7 nekiim. No nafka mina, as you said:
but it won't matter anyway because the count will have to be restarted[*].
So what's the point of the moch dachuk then?
In Halacha, this knowledge is only to know that she is mesuleket damim, according to te "stringent reasoning" explained above
Moch Dachuk is a stringent widespread minhag, advised by Shulchan Aruch YD 196, 1
But according to all poskim it's a stringency only, not a din. The lenient opinion (ziknute deRabbi) is the opinion of Rashba (Chiddushim 68b, and Torat Habait), which allow to make hefsek with bdika of the first day on morning. The intermediate stringency (Rababan in Mishna) from Ikar Hadin point of view is the Rambam, which give Chezkat mesuleket danim with a bdika of 2nd day in morning. The RAH also ruled as Rabanan; there is no hefsek at the first day in morning, for the first day we need a clean bdika in afternoon. May be that for RAH each bleeding day has a din of "first day".
This last issue, comparison between a day with bleeding and the first day according to Rabanan in Mishna is discussed by Rashba in Torat Habayt Hakatsar:
First mention in Rishonim
Rashba in Torat Habayt Hakkatsar, in the fifth Shaar, Dine Habedika Vehasefira. He told about a day which was known as with oponed source and added an advice. To be stringent for each hefsek Tahara as if there was an opened source and to watch all the ben hashmashot with a moch dachuk. This, despite that Rashba himself is the most lenient Meykar hadin. Meykar Hadin according to Rashba, if she observed a stopping of the bleeding at first day morning. She is already mesuleket damim. The Chavat Daat presented bellow addresses this with reference to a Berayta.
but it won't matter anyway because the count will have to be restarted. So what's the point of the moch dachuk then?
--> To start 7 nekiim we need to know that she is mesuleket damim at the beginning of the count. If the day before (the day of hefsek Tahara) was known as bleeding, this day has a problem of Opened Source (it is a risk day until its end) until a proof of siluk damim. If the woman made two bdikot in the morning, the first bdika was bloody and the second bdika was not bloody, it seems from the words of Tosfot that this is not sufficient to make a Chezkat mesuleket damim. Tosfot needs that the second bdika may not be before afternoon (מן המנחה ולמעלה). The Chavat Daat understood that the bdika needs to continue until the end of ben Hashmashot time (he takes the svsrat hamakshan from the Berayta, who add a layer to the Chashash of rabbi Yehuda (for morning), for a bleeding day regarding the second bdika) , i.e. a moch Dachuk. But Rishonim did not agree here with this rule. Rashba itself said that a bdika of non-bleeding in the first morning is a good hefsek. Rambam needs afternoon, no more.
Additionally see Chavat Daat at the first paragraph of siman 196