As no-one else seems to be answering this, I will post a basic answer.
The Derby Mercury newspaper of 15 July 1784 p4c3 has an advert for calico workers. Apply to Peter Nightingale Esq at Lea, or Benjamin Pearson at Lea Cotton Mill. Benjamin Pearson is frequently mentioned in the Barmaster’s Books for Cromford Liberty during the 1770s as agent for Gang Mine. He also acted as agent for Peter Nightingale in taking mines in Cromford Liberty.
The book “The Arkwrights: Spinners of Fortune” by R.S. Fitton, published 1989, on p.105 states that Benjamin Pearson had worked for Arkwright for 7 years up to 1782 when he was poached by Nightingale, who was later fined 20 guineas for this. Benjamin Pearson’s partnership with Nightingale ended on 28 March 1785.
If you consult Google Booksearch and put
“Benjamin Pearson” +Arkwright
into the search box, it will bring up Fitton’s book and one is allowed to see the relevant pages.
As for researching the genealogy of the Pearson family, this is covered in Ince’s Pedigrees which are available on the Wirksworth.org website. The genealogy is rather difficult because of the frequency of some names, e.g. Thomas Pearson, which is very common in Matlock Parish.