Are there any recent Halachic sources that discuss whether or not the Yehi Ratzons following leining would be recited a fast day that falls out on S/T/W/F?

I realize that at Why are the Yehi Ratzon prayers connected to Tachanun? it is indicated that there is something special about Mondays and Thursdays, however a similar argument could be made for Fast Days, when we say Selichos, or we could just not Pasken like the view brought there.

Are there any recent Halachic sources that discuss whether or not the Yehi Ratzons following the Torah reading would be recited a fast day that falls out on S/T/W/F?

I realize that at Why are the Yehi Ratzon prayers connected to Tachanun? it is indicated that there is something special about Mondays and Thursdays, however a similar argument could be made for Fast Days, when we say Selichos, or we could just not rule like the view brought there.

There appears to be an understanding that the Yehi Ratzons following Torah reading are said only on Mondays and Thursdays (see for example, the Artscroll Siddur). Halacha Lemaaseh, is this the case (sources please)? The Nafka Minah would be a fast day that falls out on S/T/W/F.

I realize that at Why are the Yehi Ratzon prayers connected to Tachanun? it is indicated that there is something special about Mondays and Thursdays, however a similar argument could be made for Fast Days, when we say Selichos, or we could just not Pasken like the view brought there.

Are there any recent Halachic sources that discuss whether or not the Yehi Ratzons following leining would be recited a fast day that falls out on S/T/W/F?

I realize that at Why are the Yehi Ratzon prayers connected to Tachanun? it is indicated that there is something special about Mondays and Thursdays, however a similar argument could be made for Fast Days, when we say Selichos, or we could just not Pasken like the view brought there.