I personally just use it as a way to "lurk" and observe other RPs, since my character is only using Ninja for its doofy run that I feel fits his character.
However, I have seen a couple instances of it being used in RP. One was an individual "counter-pickpocketing" another character who had lifted a gil pouch off someone. She basically just emoted what she was doing, dropped into stealth, walked over to the other person, emoted the actual counter-pickpocketing, and then walked back before de-stealthing. She used the usual non-committal descriptions to allow for the other player to react to it (which their deigned not to so as to be surprised and angry about the missing pouch instead), and it flowed pretty well.
The other way was someone stalking another character - which was actually the instance Warren alludes to above. They were first asked if they were actually stalking IC or just OOCly lurking, to avoid any confusion. Then one of the other participants - a miqo'te martial artist - emoted hearing the stalker's approach and kicked up a cloud of dust to try to reveal her. She assented via emote and an interesting conversation followed.
Overall, I'm of the feeling that you treat moving in stealth like any other potentially "offensive" (offensive in the combat sense, not "insulting" offensive) action and leave it nebulous enough to allow people to react to it accordingly. Basically, don't emote that you 100% snuck up on that Roe and stole everything but his smallclothes without him noticing and I think you should be fine. Even if the game "says" straight invisibility, I think working with it in this manner should avoid most issues.
However, I have seen a couple instances of it being used in RP. One was an individual "counter-pickpocketing" another character who had lifted a gil pouch off someone. She basically just emoted what she was doing, dropped into stealth, walked over to the other person, emoted the actual counter-pickpocketing, and then walked back before de-stealthing. She used the usual non-committal descriptions to allow for the other player to react to it (which their deigned not to so as to be surprised and angry about the missing pouch instead), and it flowed pretty well.
The other way was someone stalking another character - which was actually the instance Warren alludes to above. They were first asked if they were actually stalking IC or just OOCly lurking, to avoid any confusion. Then one of the other participants - a miqo'te martial artist - emoted hearing the stalker's approach and kicked up a cloud of dust to try to reveal her. She assented via emote and an interesting conversation followed.
Overall, I'm of the feeling that you treat moving in stealth like any other potentially "offensive" (offensive in the combat sense, not "insulting" offensive) action and leave it nebulous enough to allow people to react to it accordingly. Basically, don't emote that you 100% snuck up on that Roe and stole everything but his smallclothes without him noticing and I think you should be fine. Even if the game "says" straight invisibility, I think working with it in this manner should avoid most issues.