Two versions of his anonymous catalogue are online. One, at the British Library, was printed at Livorno in 1756, and has a number of annotations on the title-page, identifying Jackson as the owner:
The manuscripts are described on pp.625-63 and numbered separately from the printed books, 1 to 215:
Duc de la Valliere (1708–1780); as is well known, many of the duc de la Valliere's books were bought by the Marquis de Paulmy, (1722-1787), and are now in the Bibliothèque de l'Arsenal in Paris.
The other copy of the catalogue, at the Biblioteca Nazionale, Turin, printed somewhat later, includes an Appendix, paginated 1-20 (of which pp.15-20 are devoted to manuscripts):
No.43 is a copy of Bonaventura's Psalter of the Virgin written "per Fratrem Johannem de Rotondisco":
It can therefore be identified as Paris, Bibl. de l'Arsenal, ms.420:
It is now Paris, BnF, ms.lat.13686 (digitized on Gallica):
No.60 is a copy of Cicero from the library of Sozomeno with a famous inscription stating that it is better to buy second-hand books than to commission new ones, because of the expense:
It was referred to by Tilly de la Mare in her The Writing of Italian Humanists (1973), p.97, as "now lost", but re-appeared at Christie's, 25 June, 1986, lot 215. This manuscript, and the following one, no.61, both came from the library of the early Humanist Sozomeno of Pistoia:
Sozomeno's books have recently been the subject of a detailed monograph: Irene Ceccherini, Sozomeno da Pistoia (1387-1458) Scrittura e libri di un umanista, Biblioteca dell'«Archivum Romanicum» - Serie I: Storia, Letteratura, Paleografia, 431 (Olschki, 2016). Several Sozomeno-Jackson MSS can be identified by searching Irene's Sozomeno website here: http://sozomeno.fondazionecrpt.it//biblioteca.php
Jackson's library, especially his manuscripts, is currently being studied by Francesca Masi. Anyone with information about their current whereabouts is encouraged to contact her, or me.