First up I'll have to equate a few terms to avoid confusion.
I'm going to equate your concept of "instigator" with "causer". And your concept of "agent" as "causee"
(1) If I use 行く with another verb as its purpose, is を available to mark the agent? It seems like this should be the case since お弁当を should be connected to 行く。
Compare:[a] 子供にお弁当を買いに行かせます。( (Causer/Instigator) let the child go to buy 弁当)
[b] 子供をお弁当に買いに行かせます。(Cannot be parsed)
This portion has nothing to do with the causative construction. 弁当に買う is grammatically wrong because 買う is a transitive verb. It has to be 弁当をかう.
Also, it is okay to have two にs in the sentence because they are different にs. 子供に marks it as a relational/indirect object. 買いに marks purpose of action. (Also take a look at sawa's answer to another question)
Now lets look at 1[a]. Is を available to mark the agent?
No. This is because you cannot have more than one を appearing in a clause. The causee (in your case the "agent") can be marked only by に because を has already been used once in 弁当を買う
(2) With intransitive verbs, must I use を to mark the agent?
Compare:[a]その人は私をそこに座らせました。(That person let me sit there)
[b]その人は私にそこに座らせました。(That person let me sit there)
EDIT: (My intuition says that そこに座らせます is fine, but 私にそこに座らせます is not. I think it should be 私にそこで座らせます instead, or else I'd have two にs performing "indirect object" role. Please someone let me know in the comments if I got this portion right/wrong)
Yes 私を has to be used if you want to maintain the use of そこに.
(3) If I leave off the object of a transitive verb due to ellipses, may I mark the agent with を? (This seems strange, but I figured I'd ask.)
Compare:[a]子供に買わせました。( (Causer/Instigator) let the child buy (something) )(Assuming sufficient context)
[b]子供を買わせました。( (Causer/Instigator) let (Somebody) buy the child)
Again nothing to do with the causative construction. 子供を買う means "to buy the child" and not what I think you think it means.
(4) If I use a transitive verb, but use を to mark something that is moved through or done with effort, may I still mark the agent with を?
Compare:[a]子供に道を行かせます。
[b]子供を道を行かせます。
[c]彼に私のことを分からせます。
[d]彼を私のことを分からせます。
No. As in (1), you cannot have を appearing more than once in a clause.
EDIT: In 4[c] and 4[d], I dont think they're grammatically correct. 分かる is an intransitive verb i.e. it cannot be ことを分かる. I think a better way to express it would be:
[c'] 彼に私のこと｛について・にかんして｝分からせます。
[d'] 彼を私のこと｛について・にかんして｝分からせます。
(5) I've also heard mention that some speakers occasionally use を to mark the agent with intransitive verbs without any further details. Is this something that a seemingly random group of people does? Is it due to dialectal variation? Is there a pattern to when it can be done? Is there a difference in nuance?
In the cases where I can choose between marking the agent with を or に, is there any difference in nuance?
In a fairly old grammar, I've read that using に may soften the statement a little.
Choosing to use に or を can mean different things. The exception to this rule is that you cannot use を more than once in a clause.
The difference between を and に lies in the agent/causee's volition.
When に is used, the causee does the action in line with his volition.
When を is used, it is independent of the causee's volition. This means it can have the nuance of being forced. (Although may not always be the case, it depends on context)
So (2)[b] (if grammatical) means that "you" intended to sit there, and that person let you. (2)[a] can also mean the same thing, but it can also mean that that person forced you to sit there.
Now two questions are begging to be asked:
- "When we have no choice but to use
にbecauseをhas already been used once, how do we know if the action is in line with the causee's volition or not?" - "Then how do we express "being forced to ~" unambiguously?"
The answer to 1. is that we can't. We have no choice but to guess from the context of which the sentence is being used.
And 2. To express "being forced to ~" we can use the causative-passive construction:
その人は私をそこに座らせられる。(That person made me sit there)
