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I try to use the 2nd or 3rd definition of words (to slow down speed readers). However, I am not sure if "ignorance" has a 2nd definition.

(common meaning) is "a lack of knowledge". With this meaning, no syllable is stressed.

• My ignorance of hardware means I cannot build my own pc.

(2nd meaning?) If pronounced differently, I think that "ignorance" can also mean "a willful and careless disregard of something". The "nor" syllable in "ig-NOR-ance" must be stressed.

• 
  The French were aware of the strategic weakness of the Maginot Line, and their ignorance of it enabled the German blitz through the Low Countries.


• My ignorance of my girlfriend's hourly text messages quickly caused our break-up.

In a dictionary, "ignorance" is only defined as "lack of knowledge". But, I am not talking about that "ignorance". I am talking about the "ignorance" that is derived from "to ignore" and thus pronounced just like "to ignore", and thus has the meaning of "to ignore". There is precedence for this:

"to accept" --- derive ---> "acceptance"

"to ignore" --- derive ---> "ignorance"

....

Anyone agree with me?

Most dictionaries show usages which are reasonably common, to explain what might be happened across. Thus there is a lower limit, below which a particular dictionary might not mention a usage even though it has been used.

The OED's lower limit is very low; it's a historical dictionary. Ignorance appears in three main senses:

1.
a. The fact or condition of being ignorant; want of knowledge (general or special).
b. Constr. of (†in, or subord. clause).
c. With an and pl.: An instance or example of ignorance. rare.

†2. With an and pl. An act due to want of knowledge; an offence or sin caused by ignorance.
3. (In full the time or days of ignorance; tr. Arabic jāhilīyah state of ignorance, < jāhil ignorant.) The period of Arabian history previous to the teaching of Muhammad.

This doesn't mention your usage at all, even as an obsolete sense (with a dagger mark) which could possibly be revived.

So no, ignorance doesn't mean ignoring. Ignorance only means lack of knowledge, and has never meant the deliberate act of ignoring. So you would need to use that word.

My ignoring of my girlfriend's hourly text messages quickly caused our break-up.

OED shows the etymology:

< French ignorance (12th cent. in Littré) = Italian ignoranzia, Spanish ignorancia, < Latin ignōrāntia, < ignōrānt-em ignorant adj. and n.

...and ignorant there simply means "one who has no knowledge" of something.

It is in fact ignore which has changed its meaning over time. OED has first the obsolete sense related to ignorance:

†1. trans. Not to know, to be ignorant of. Obs. or rare.

Over time, ignore has become rather more deliberate. One has no knowledge of something because one has chosen to have no knowledge of it.

Ignorance has not followed this path.

I don't see a second definition either. However, as I expect you would know, ignore is a verb that would enable you to say "My ignoring of my girlfriend's hourly text messages . . ." That would convey that you made a decision to not expose yourself to the information.

"Ignorance" doesn't generally imply willful lack of knowledge. If you stress the NOR, it would be clear what you meant in speech, but for writing, I would use "By ignoring my girlfriend's hourly text messages, I quickly caused our break-up." It's not only has clearer meaning, but also a more active voice. You might also consider "neglect" if you want to imply that reading the texts was an unfulfilled responsibility.

There appears to exist confusion between the noun ignorance and the verb ignore as well as how to use these words in a sentence.

The word ignorant is an adjective describing a person in a state of unintentional or deliberate unawareness.

ig·no·rance ˈiɡnərəns/ noun: lack of knowledge or information. "he acted in ignorance of basic procedures"

synonyms: incomprehension of, unawareness of, unconsciousness of, unfamiliarity with, inexperience with, lack of knowledge about, lack of information about;

antonyms: understanding, familiarity, knowledge, education

versus

ig·nore iɡˈnôr/ verb: refuse to take notice of or acknowledge; disregard intentionally. "he ignored her outraged question"

synonyms: disregard, take no notice of, pay no attention to, pay no heed to;

more: fail to consider (something significant); "direct satellite broadcasting ignores national boundaries"

legal: (of a grand jury) reject (an indictment) as groundless.

Given these famous quotes:

"The ignorant can be educated, but you can't fix stupid."
- (approximated) possibly Mark Twain?

“We are all born ignorant, but one must work hard to remain stupid.”
― Benjamin Franklin

“Being ignorant is not so much a shame, as being unwilling to learn.”
― Benjamin Franklin

"If we're looking for the source of our troubles, we shouldn't test people for drugs, we should test them for stupidity, ignorance, greed and love of power.”
― P.J. O'Rourke

It's clear that we generally agree that stupid means incapable of learning, but ignorant means different things to different people. (Or even the same person, in the case of Ben Franklin. :)