How could you describe the nature of Booker T. Washington's influence in helping, enlightening, and sustaining the narrator in Invisible Man?

In the first Chapter of Invisible
Man, "The Battle Royal," the Invisible Man wants to be a young Booker T.
Washington.  The speech he gives to the white members of the Southern town's social
elite is filled with Washington's rhetoric:

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We of the younger generation extol the wisdom of
that great leader and
educator.

But, he switches
rhetorical modes and starts to sound like W. E. B. DuBois, a more outspoken Black
activist of the time, an enemy to Washington.  He says: "Social euality" (DuBois)
instead of "social responsibility" (Washington).

This
rhetoric is too harsh for his white audience; they don't want to hear a black man
demanding equality.  They expect him to be submissive and talk only of hard work, like
Washington, not the political demands of DuBois.

To use a
Malcolm X analogy: Washington is like the "House Negro": he is a moderate, acquiescent,
advocating slow steps toward progress, playing by the rules.  DuBois is a "Field Negro":
he hates his status and wants his freedom immediately and is willing to openly disobey
white society.

So, the Invisible Man is caught between the
two, caught up in the words of his grandfather:

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I'd overcome them with yeses, undermine them with
grins, I'd agree them to death and destruction. Yes, and I'd let them swallow me until
they vomited or burst wide
open.

His grandfather looked
and sounded like a Washington, a house negro, but he was really a DuBois, a house
negro:

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Grandfather had been a quiet old man who never
made any trouble, yet on his deathbed he had called himself a traitor and a spy, and he
had spoken of his meekness as a dangerous activity. It became a constant puzzle which
lay unanswered in the back of my
mind.

So, the Invisible Man
will spend most of the novel trying to find identity and freedom in the smalls steps
advocated by Washington (work) and the bold moves advocated by DuBois (the Brotherhood).
 Neither work: he is still invisible.  Unfulfilled, he finally rebels at the end and
becomes an Invisible Man, waiting, hiding, hopeful to emerge one day as seen by himself
and society.