I think that players should be able to handle this without a GM telling them anything. I am not even sure if GMs can reliably determine whether or not you feel that your character can or can't linger. The person best equipped to make this call is the player.
You really have two possible situations and I think you should be choosing between them from based on your character's personality and the IC situation.
If your IC situation makes you feel comfortable ICly waiting fort the NPC to have time, feel free to wait and try a few times. If the GMs notice and have time, they will grab the puppet. If they don't respond, submit a puppet request if needed.
If your IC situation makes you feel that you can not linger, then don't. Tell the NPC something like, "Mano. Sorry but I can't stick around. I got bakas on hunting for me right now. But we need to talk. I'm Hunted on SIC. Phone number's 123-4567." Then get out of there and submit that puppet-request.