I would not try to teach "join up" on a lunge line. Becuase, if they learn to come in to you when they stop, this will become an annoyance if and when you just want to lunge your horse in the future, and every time you stop to change direcions or whatnot, they try to come in to you.
When you described in your first post that you stopped and turned away from yourhorse, then looked back and he was just standing there, you were frustrated becasue he had not made the choice to come in to you.
Well, at that point, you do something that forces him to make another choice.
All you have to do is get him to break out of that "trance" of indecision. It can be hardly anything, like scuffling your foot, or tapping your boot with the whip/rope. Anything that make him choose to move his feet.
Once he moves his feet, you STOP. Wait and see, he might choose to come to you. You can encourage that choice by turning partway away from him and lowering yoiur head a bit. IF he runs away, then drive him a bit, then stop your feet/turn off your drive, and wait and see if he chooses to come in to you.
Whenever he stops and gets stuck (can't decide), you offer him aother opportunity to make a choice.
However, if he's looking at you, he might be "searching" for the right answer to this situation that he's in. Give him some time if it looks like he really is weighing his opitions and trying to fidn the right answer. Don't force him to decide too soon, if he is already searching mentally.
But, if he is "stuck", he searched and searched , or he is looking at you but pretty sure that he still wants to run away, then, you interrupt that "stuckness" with the scuffle of the boot, or the wigge of the whip, or whatever (the littlest amount necessary to break up his stuck thinking and make him move his feet. Do not go straight back to massive driving)
This is he "draw". You work on the draw as much as the drive. The draw is probably mre important.