Brilliant!

Let us follow the dictionary order and see which page the word "BRILLIANT" is on.

First, we will go through all words that start with A.

Next, we go to B, where BRILLIANT is located.

Since the word begins with BR, we go through all words that begin with BA, BI, BL and BN

After that, the word begins with BRI, so we go through all words that begin with BRA

Then, the 4th letter is L, and we go through all words that begin with BRIA and BRII

Then, the 5th letter is L, so we go through all words that begin with BRILA and BRILI

Next, the 6th letter is I, so we go through all words that begin with BRILLA

Finally, the last 3 letters in BRILLIANT follow the alphabetical order, so we know that the next page after all the pages in front will contain the word BRILLIANT. We need to add all pages in front and add $1$ for the page BRILLIANT is in.

Now, we need to count all the words available in the conditions above:

Words that start with A (there are 2 I and 2 L) $=\dfrac{8!}{2! \times 2!} = 10080$

Words that start with BA (there are 2 I and 2 L) $=\dfrac{7!}{2! \times 2!} = 1260$

Words that start with BI (there are 2 L) $=\dfrac{7!}{2!} = 2520$

Words that start with BL (there are 2 I) $=\dfrac{7!}{2!} = 2520$

Words that start with BN (there are 2 I and 2 L) $=\dfrac{7!}{2! \times 2!} = 1260$

Words that start with BRA (there are 2 I and 2 L) $=\dfrac{6!}{2! \times 2!} = 180$

Words that start with BRIA (there are 2 L) $=\dfrac{5!}{2!} = 60$

Words that start with BRII (there are 2 L) $=\dfrac{5!}{2!} = 60$

Words that start with BRILA $=4! = 24$

Words that start with BRILI $=4! = 24$

Words that start with BRILLA $=3! = 6$

The word BRILLIANT $=1$

The page number BRILLIANT is on $=10080 + 1260 + 2520 + 2520 + 1260 + 180 + 60 + 60 + 24 + 24 + 6 + 1 = \boxed{17995}$