Good God, pilots over think this and make it more than it is. "XXX, on the go, request closed?" TWR can say, L(R) Closed approved, report base" OR, they can say, Contact departure on XXX.xx for sequence". You call departure, they put you back in the queue for a visual. If you're at a busy radar terminal, expect the latter; quiet tower field in Podunk, the former. Done both. It isn't more complicated than flying the plane, children of the magenta line.
GF