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I don't believe it is either the verb or the tense that expresses any action that has recently stopped.
Your examples could have been continued in different ways to show the reverse situation:
Action still continuing: I've been painting the room all day, and I intend to finish in the next two hours.
Action recently stopped: It's been raining for two hours, but it's stopping just now.
There is also a way in which "have been going to the tanner's" is
continuous. Simply paraphrase it as "have been in the habit of
going to the tanner's". I suppose your student thinks it means
something like "have been on the way to the tanner's". In that
case, you'll need to explain that one meaning of "go" is "visit
regularly", and that since the place visited (the tanner's) features
prominently in the sentence, it makes sense that the "visit regularly"
meaning is most likely in this context.
There is nothing ungrammatical about the variants you quote.
I've been going to the tanner's for two hours.
I've been going to the tanner's all day.
As you say, it just doesn't make sense, because of assumptions we have about how frequently people usually go to a tanner's.
CJ
P.S. I trust you aren't talking about specialists who turn animal
hides into leather. But wait! The result can be
practically the same, can't it?