Alot of the qualities Jagex seeks in their Player Mod candidates, are the same qualities that the Sythe staff would seek in new staff members on this website. There are obvious ones like honesty, integrity, people who follow & respect the rules, as well as report other people who are breaking them, people that are thoughtful, friendly, and generally helpful to other players etc.
But I know that Jagex also selects their Player Mod's based on actively reporting people breaking the rules. This does not mean reporting every little thing that somebody does wrong, or every time somebody says a swear word, but the players who legitimately report rule breakers in a genuine attempt to make the game a better experience for everyone. I've also heard that they heavily emphasize account security, and so they look for people who have a bank pin & recovery questions set, and who actively change their passwords every few months.
EDIT: I forgot to mention that good grammar is a huge bonus to increase your chances of becoming a Player Mod. You almost never see Player Mods who have horrible spelling/grammar, as these players are expected to be role models for the rest of the community and so if they don't sound intelligent when they speak, its unlikely people will listen to them or take them seriously.
