"Now were the sticklers in a readinesse, and the combattors with their weapons drawne fell to it, so that betwixt them were striken six or seuen blowes right lustilie."
Raphael Holinshed Chronicles of England, Scotland, and Ireland London, 1587, Volume 6, p. 992 (describing a 1548 duel)
"Thus talked Basilius with Zelmane, glad to make any matter I subject to speake of, with his mistresse, while Phalantus in this pompous manner, brought Artesia with her gentlewomen, into one Tent, by which he had another: where they both wayted who would first strike upon the shielde, while Basilius the Judge appointed sticklers, and trumpets, to whom the other should obey."
"But Basilius rising himselfe to parte them, the sticklers authoritie scarslie able to perswade cholerike hearers; and parte them he did."
Sir Philip Sydney The Countesse of Pembrokes Arcadia Cambridge 1912 (First printed 1590)
"A stickler betweene two, so called as putting a sticke or staffe betweene two fighting or fencing together."
John Minsheu, Ductor in Linguas 1617
This seems very similar to:
"But the two lieutenants shall have in their hands either one a spear without iron to separate them if the king will make them leave off in their fighting, whether it be to rest them or other thing whatsoever pleases him."
The Ordinance and Form of Fighting Within Lists
These men are called ascotes in the contemporary English account of the combat between Lord Scales and the Bastard of Burgundy, and écoutes in de la Marche's account of the same combat, as well as in descriptions of other combats on the continent.
"I styckyll between wrastellers (wrestlers) or any folkes that prove mastries, to see that none do other wronge, or I part folke that be renay to fight. Je me mets entre deux."
John Palsgrave L'esclarcissement de la langue francoyse London 1530
The earliest example of stickle or stickler in this sense that I can find is Palsgrave, in the context of wresting, and umpires in Cornish wrestling are still called sticklers, and still carry sticks.
A scrupulous umpire would be strict and unyielding in the application of the rules, and so we see the roots of stickler in the ordinary sense used today.