John Segundus is, to begin with, a purely theoretical magician and a member of the Learned Society of York Magicians. He played an important supplementary role in the Revival of English Magic, bringing Gilbert Norrell into public awareness, encouraging Jonathan Strange to meet with Norrell, and caring for and eventually healing the enchanted Lady Pole.
Early life and the York Society
It is not clear where Mr Segundus comes from, but from remarks in his opening address to the Learned Society of York Magicians he appears not to be a Northern Englishman by birth; certainly some three years before his arrival in York he is in London .
Before Segundus joined the Society he wrote A Complete Description of Dr Pale's fairy-servants, their Names, Histories, Characters and the Services they performed for Him in 1799, which Norrell later described as "a creditable piece of work" . Rare praise indeed from a proficient who generally slighted the learning of other magicians! tho' a little spoiled by Mr Norrell's proceeding to point out an omission.
Segundus joined the Society in early Autumn 1806, and raised the question of why magic had left England. Despite strong criticism from some other members, Segundus and another Society Magician, Honeyfoot, investigated the matter on their own. They approached Gilbert Norrell, a Yorkshire magician who had recently turned down an offer to join the Society. To their surprise, they found that his magical library was by far the most extensive they had seen, and, even more unexpectedly, that Norrell described himself as a practical magician. Segundus and Honeyfoot succeeded in bringing Norrell's abilities to the attention of the Society, which culminated in the magic of The stones of York .
Segundus was the only member of the Society to continue his career as a magician afterwards. At the behest of John Childermass, Segundus wrote an article to the newspaper The Times, "EXTRAORDINARY OCCURRENCES IN YORK: AN APPEAL TO THE FRIENDS OF ENGLISH MAGIC", which brought Norrell's achievement into public awareness . The influential periodical The Friends of English Magic took its name from Segundus' article .
While Mr. Segundus was most certainly a gentleman he was unfortunately of straitened means, and for a time resided in the garret of Mrs. Pleasance's lodgings in Lady-Peckitt's-yard, which as those who know York well can tell us, is just off Fossgate. He also took various employments to supplement his income, though these were generally thwarted by some ill-luck or other: his thriving career as a schoolmaster for example was destroyed by Mr Norrell, who implacably resented all attempts to teach others the art of magic .
In person Mr. Segundus was of a neat figure, with a self-effacing manner. Jonathan Strange describes him aptly on first seeing him:"A small man with hair and eyes so dark as to be almost Italian - though the hair has grey in it. But the expression so quiet and timid as to be English without a doubt!" 
Shadow House and Strange
In July 1809 Mr Segundus, accompanied by Mr Honeyfoot, visited Shadow House, where they stumbled upon Jonathan Strange attempting a summoning spell. (Segundus in particular, whose magical sensibility was much the stronger of the two, was so attuned to the magic that he ultimately interrupted the spell.) As it turned out they were the first fellow magicians that Strange had met since he began his career. They all three met that night to dine together and in the course of the evening convinced Strange to meet with Norrell in London, spearheading the first magical collaboration in centuries . Segundus and Strange remained friends, and often corresponded  .
Due to pecuniary embarrassments, in the Autumn of 1815 Mr Segundus set himself to look for work. He began by tutoring in theoretical magic and then, at the behest of the father of one of his pupil's, went on a commission to Starecross Hall. There he met the owner of the estate, Mrs Lennox, who upon hearing of Segundus' profession (and at the same time making her usual sharp assessment of his character and qualities) offered to help him create a school for magicians at Starecross. Unfortunately Mr Norrell did not approve the idea, and meanly used his influence to crush the enterprise .
Shortly after Norrell's interference Segundus and his patroness decided instead to establish a madhouse at Starecross. Their first patient was Lady Pole, whom Segundus immediately recognized to be under an enchantment of some kind but whose true situation he did not then fully understand . In February 1817 however Segundus, with the aid of John Childermass, succeeded in breaking the enchantment by using Martin Pale's Restoration and Rectification to restore Lady Pole's missing finger - the object that represented her entrapment. The magic was in large part made possible by the return of magic to England, initiated (at least nominally) by Jonathan Strange .
As mentioned above, the first work by John Segundus of which we learn is A Complete Description of Dr Pale's fairy-servants, their Names, Histories, Characters and the Services they performed for Him, (1799). Mr Segundus, though a deeply modest man, has laboured mightily over this book and is justly proud of it. We hear of it when Mr Norrell - having no doubt read it in his usual spirit of jealous anxiety, lest any man's knowledge of magic might possibly equal his own -- finds fault with it .
In 1820 Segundus' book The Life of Jonathan Strange was published by John Murray in London. It contained many novel details of Jonathan Strange's character, for example describing his preference for clever female company , his attempts at poetry , how he was influenced by The Duke of Wellington , and how he inadvertently played an enormous role in the victory at Quatre Bras .
Mr Segundus was a bachelor during the early Revival years, and it seems has remained one .
Mr Segundus has a finely-tuned sense of direction .
Mr Segundus is by nature acutely alive to magical manifestations, to the extent that he feels faint when in the presence of magic ,  . Later the aura attending the enchanted Lady Pole is enough to disrupt his senses. In this particular he resembles John Childermass, who possesses the same faculty to an even greater degree.