Bally Heck, I am paying full attention. I don't doubt that you will carry out the instruction the way it was intendet.
You are obviously not paying attention to what I say. I don't find the wording ambiguous. When I read it there is no doubt in my mind that it's a continous climb for several reasons, besides the obvious that you apparently also see since you do understand the instruction.
First reason is because you are not instructed to level off.
Secondly it says climbing. As I argumented earlier you can be doing anything if you have stopped doing it already. If you had stopped your climb the next sentence should say something like "turn left to.. then climb to..". You are climbing and you shoud continue your climbing to whatever.
Thirdly, it not a Haynes manual for an old Morris Minor, you don't read one sentence at a time before carrying out the next. You should read the entire instruction in it's full length instead of taking it apart. I think it's a completely logical punctuation, otherwise the sentence would be so long that it would be almost completely unreadable.