Simply stated, backlash is the clearance between the transmission counter gear (sometimes called the "cluster" gear), and the PTO gear that engages it. When the PTO is shifted into mesh with the cluster, there will be a slight amount of free play between the gears. If the gears bottom out, they will be noisy, and/or the PTO will be difficult to engage. If the clearance is too great, the gears will whine or rattle from the slack between the mating teeth. Ideally, the gears should mesh with a minimum of slack, and the noise should be at a minimum at that point. Now, here's the kicker- - - - -used gears develop a "wear pattern" from long term running in a particular position, and a change from that relationship, even if the new clearance is technically correct, can cause a whine due to the established running fit being disturbed. You might have to shim the PTO in or out to get the quietest operation, even if the slack between the meshed gears is a bit more than ideal. Virtually all PTO's have a method of checking gear clearance through some type of access hole that allows you to monitor the gear movement. Most often, it's done by removing the grease fill plug and adapting a dial indicator to contact a gear tooth.
Jerry