waiting close by

[güey]

(1) Another batter waiting to take his place and being close by. (to is not "in order to")

No, the whole phrase waiting close by indicates a purpose. You can't split it up.
... waiting close by in order to take his place.

I'm waiting to go into the theatre.
I'm waiting for the theatre doors to open.

What am I waiting for?
For the theater doors to open.

Why am I waiting (for that)?
To walk into the theater.
(purpose)

 

[Piscean]

I just learned a new term: i"nfinity of purpose".

... infinitive of purpose.

 

[Tarheel]

Yes, that.

 

[jutfrank]

I accept that the answer to "Why are you waiting?" is "Because I want to go into the theatre but the doors aren't open yet", but I wouldn't be able rephrase my sentence to "I'm waiting in order to go into the theatre".

Right. It's important to distinguish those 'purpose' phrases that function as complements from those that are adjuncts.

When they're adjuncts, they can be removed from the sentence without changing the essential meaning of the prior clause and can be replaced by the phrase 'in order to'. When they're complements (as is the case here), they cannot be removed or replaced with 'in order to'.

My view has always been that the way to classify these things is based on the meaning, not the syntax.