Ah -- got it.

But, 4.2.2D (based on your description; I don't have and we don't use the manual) only says "each official administers the throw-in on the line s/he is responsible for."

L can meet that requirement either by bouncing the ball as L, or as moving up to T and having T move down to L. Does the manual say when to use each of these procedures?

Yes, it does.

By the NFHS book mechanics: If the ball is remaining in the FC and the throwin spot is on what was the L's line and the throwin spot is below the FT line extended, the L remains L and bounces the ball to the thrower. If the spot is above the FT line extended but still in the FC, the L moves up to T (and the T to L). If the throwin spot is in the backcourt, the T moves across to administer the throwin.

Yes, diagrams 4-8, 4-9, and 4-10 illustrate positioning. 4-9 is the one that directs the L and T to slide up/down.

thank you both. That's what I thought. And, so it's the answer to the OP, unless his state / local association has some specific different mechanic.

And, what I thought was also the IHSA position, until I re-read the .ppt for IL (which moves the "boundary" from the FT line extended to about 9.5 feet closer to the endline).