My experience is that the Flagstaff/Shamrock exterior lengths include the tongue.
While you wait for someone who has your exact model trailer I'll give you my measurements compared to the brochure length to give you an idea of what you might expect.
We have a 233s and its exterior length by brochure is 23'9".
The box, including the tongue, but not the bumper or spare tire is slightly less than 24'. The bumper and spare add 16".
So, if you trust it, that means the brochure exterior length includes the tongue.
Two things you can do to check this: Call the dealer and ask them to measure it. Search here for owners of the trailer you want to buy and send a PM. Not everyone is on the forum every day.
DW, 3 Kids and our Goldens
2012 Shamrock 233S
2008 Toyota Sequoia 5.7L 4WD