Little is known of Keyser's life outside of his astronomical observations and East Indies voyages. After several trips, one to Brazil, and one to Nova Zembla, Keyser participated as the chief navigator and head of the steersmen for the first Dutch voyage to the East Indies (the "Eerste Schipvaart"), which left Texel with four ships on April 2, 1595 under Cornelis de Houtman. He had been trained by cartographer Petrus Plancius in mathematics and astronomy. Plancius, a key promoter to the Dutch East Indies expeditions, had instructed Keyser to map the skies in the southern hemisphere, which were largely uncharted at the time. When the fleet finally was able to obtain fresh supplies at Madagascar on September 13, 71 of the 248 sailors had died, most of scurvy. The surviving crew stayed for several months on the island, to recover and make repairs, at which point Keyser probably made most of his celestial observations. He was aided in this by Frederick de Houtman and Vechter Willemsz. After leaving Madagascar, it took another four months (February to June 1596) for the ships to reach Sumatra and finally Bantam on Java. Trade negotiations went sour, perhaps caused by Portuguese instigators, perhaps by inexperience, and the crew was forced to find drinking water and other supplies on Sumatra across the Sunda Strait, at which crossing Keyser apparently died. On August 14, 1597, 81 survivors made it back to Texel, including de Houtman, who probably delivered Keyser's observations to Plancius.
From Keyser and de Houtman's observations, Plancius created twelve new constellations of the southern sky that have become accepted as modern constellations. The majority were named after various beings that 16th century explorers had encountered (e.g. Bird of Paradise, Chameleon, Toucan, Flying Fish). They were published on Plancius' celestial globe of late 1597, which was published by Jodocus Hondius. Willem Janszoon Blaeu copied these constellations on a 1602 globe and created a new globe in 1603 based on de Houtman's observations during a second voyage to the East Indies. Johann Bayer copied the southern constellations from a Plancius/Hondius globe in his 1603 Uranometria star atlas, crediting charting to a "Petrus Theodori", but not acknowledging their earlier publication, and is therefore often mistakenly credited for introducing them.