Yitzchok Isaac (1st Kaliver Rebbe) Taub - Who wrote the words for "Szól a kakas már"?

Hi all,
After overlooking an old family tree I have came across an interesting piece of information. I’m hoping it could shed some light on an still possibly unknown mystery. My 4th great-grandmother who was called Judith Purjesz nee Manheim was supposedly born in 1784 in Mako, Hungary according to all the records we came across. However according to the old family tree she was the sister of a famous Talmudic scholar or Rabbi from the village or town of Kalo, His name is not mentioned but in the translation it says that he was well known as the "Gaon of Kalo" or the Sage/Genius of Kalo. It is written in the tree that he wrote the words to the song: "Szól a kakas már". After I typed the song in google I found a Wikipedia entry which stated the man who composed the song was indeed Yitzchok Taub (the 1st Kaliver Rebbe" from Nagykallo or simply Kallo. However nowhere on the internet can I find a reliable source especially in a English which states who wrote the words for the song only the name of the composer. I am sceptical that this man is Judith’s brother even if he did write the words to the song due to the big age disparity, there is around 30 years difference between them. Judith was married to Adam Purjesz otherwise known as Adam Burjes son of Aron who was born in 1777 in Hungary.