I would like to offer some additional information to supplement Napier's biography.
First, when John settled down at Merchison Castle after a peripatetic interlude, he displayed his real inventive spirit. His property abutted lands of the king. Napier was making heroic efforts at cultivating his lands (1571-79), but his seeding efforts were constantly thwarted by huge flocks of doves which were kept on the adjacent royal property. John soaked pieces of bread overnight in good whisky. About half of the quantity he scattered around a newly seeded area and the other half was used as bait in a series of small paper cones which Napier had lined with "bird lime." Of course, the inebriated, birdbrained doves managed to stick their beaks into the wrong places and Napier collected several score and held them at ransom until he was paid the full value of all the seed he had lost.
I can offer no confirming references, but I believe that Napier was 13 when he entered St. Andrews and he can't have been much older than that when he left, without a degree. He wrote two Mirifici Logarithmorum Canones the second, Mirifici Logarithorum Canonis Constructio having been published posthumously. It was important because it described the methods he had employed to arrive at his invention.
I believe that Napier's Plaine Discovery &c., &c. was less important (to Scottish ecclesiastical history) than his dedication of the work. That was in the form of a letter to the king (whose doves ate &c., &c., &c.)