Imperial Problem Child-verse During those long(ish) stretches without communicating with the Executor, does Luke ever use their bond to reassure Vader that he's ok? Or ask odd-ish questions? ("Palpatine doesn't own any property on Naboo. Right, Father?")
Normally I’d think that actual communication over their bond would be somewhat limited by proximity (such as being in the same solar system), but then there’s that deleted scene from Return of the Jedi where Vader is, essentially, telepathically poking Luke like “Hey. Hey son. Hey son, can you come to the dark side real quick?”
While Luke is just staring at the wall with this expression like “I’m working, Dad!”
So in that case, he probably does poke at the bond every now and then. Sometimes it’s a just checking that you’re not in the vicinity because we need to not be shot at right now– no I’m not telling you where we are! thing.
Sometimes it’s a I feel conflict, and possibly pain, is everything alright, Father? (cue the bi-weekly “join the light/dark side” conversation)
Other times it’s just casual stuff. Questions about his mother, nerdy talks about ships, random observations about weird wildlife. Humorous commentary on politicians. Sometimes these come in the middle of Vader trying to give orders, and they’re a little distracting, but hey Luke is talking to him, he’s not going to complain.