Much of that is problematic, but I’ll take a shot anyway.
“To last long” means to happen for a long time.
“To take long” means to be far away in time or to take much time to do something. For your purposes, both work, which is not always true. I get to that at the end, so I added this up here.
You seem to mean either this
If they neither offer you something nor ask something of you, then wait. It won’t take long.
Or this
If they neither offer you something nor ask you something, then wait. It won’t take long.
I used “something” generically because both verbs require direct objects, and you have provided merely indirect objects. I cannot say “I offer.” That’s not complete. I must, for example, say “I offer help.” Similarly, I cannot say “I offer the stranger.” That is the equivalent of “I offer to the stranger.” What do you offer?
“To offer a person” (with person as the direct object) means something entirely different from “to offer something to a person.” I strongly doubt you mean the former.
“If they neither offer you something nor ask something of you” is not a sentence by itself. That is a mere subordinate clause. That is why I connected the next thought, the main clause, to it with a comma. I can do this because “if” is the type of conjunction that allows this. Note that I then ended the complete sentences with a period.
The first sentence and the statement that it won’t last long must be connected by more than a comma. A comma alone is no conjunction. It’s increasingly common to combine closely linked thoughts this way, but it doesn’t pass strict grammatical tests. You need some variant of the conjunction “because,” a semicolon or a separate sentence. The last two work just as well as “because” here because the thoughts are so closely connected that the relationship will be understood without “because.”
“To take long” and “to last long” are sometimes synonyms, but they can also be quite different. In your sentence, they are more or less interchangeable.
Wait, because it won’t take long for them to offer or ask something.
Wait, because their failure to offer or ask something will not last long.
Either of these ideas is what is actually being understood, and since they are just about equivalent in meaning, you can swap the verbs in your sentence.
That is not always true.
The economic rebound will not last long. - The duration of the rebound will be short.
The economic rebound will not take long (to occur). - The event will happen soon or in a relatively brief amount of time.
“To last long” means to happen for a long time.
“To take long” means to be far away in time or to take much time to do something.
Getting dressed for work doesn’t take long. - The time it takes to get dressed is relatively short.