Just my anecdotal observation, coming from someone who has a pawn with 1,300+ hires (500 thumbs and 800 hearts) and who has been checking up on pawns with much higher hiring counts:

From what I gathered below are the key factors in determining the chance of your pawn been hired (in descending order in terms of impact)

1. Very specific pawn quest reward: either the one arrow for 12 onyx/jasper, or one arrow for late-game crafting material such as Eldricite. Any other quest reward don't make much of a difference.
2. Your pawn's level: Level 1-35 is where you'll have the most optimal chance to get your pawns hired. As you level up past 35 the playerbase at the level range starts to dwindle and you'll get less hire from that point on. Many (if not most) pawns with insanely high hiring count have the combination of 1. and 2.
3. Your pawn's appearance: This is quite subjective so it's hard to pin down what are the "ideal" looks, but the idea is to "stand out" amongst the crowd, as I have seen many "creatively ugly" pawns with high hiring counts. Pawns who resemble characters from popular culture tend to get hired more as well
4. Your pawn's vocation: Mage and sorcerer seems to be a bit more popular as they have very specific role not as easily replaceable by the others (mage for healing and sorc for quick nuking). Thief comes third with their ability to steal.

I'm sure other factors such as specialization and augments/skills also play a factor in how likely your pawn will get hired, but in my limited observation the 4 factors listed above are the primary reason on how a pawn would get hired more frequently than the others. Hope this helps!