Why weren't there any northern tribe waterbenders among the invaders during the solar eclipse?

Question

The Team Avatar, together with many enemies of the Fire Nation, prepared for an invasion into the heart of the Fire Nation during a solar eclipse which robs firebenders of their bending, making them defenseless. Led by Hakoda (Sokka's and Katara's father) many southern water tribe soldiers (all of whom are non-benders except Katara), foggy swamp waterbenders, earthbenders and others participated in the invasion, however there were no waterbenders from the northern water tribe, not even at least master Pakku or water king Arnook (Yue's father).

Sokka had asked his father Hakoda to reach out for certain individuals the Team Avatar knew and Hakoda stated he did so with all of the participants Sokka asked for. I wonder why master Pakku or the northern tribe waterbending army weren't among them, which would make it much easier for the invaders before and after the eclipse to conquer the capital city.

Were the invaders so sincere in their plan to attack a defenseless Fire Nation during the eclipse that they didn't bother with a too big army?

In fact, they underestimated the Fire Nation which prepared for such an attack when it would be weakened by the eclipse.

Or since the Northern Water Tribe seems to value morale, tradition and honor, was it clear they wouldn't participate in such an honorless attack?

When the Team Avatar met the masters including Pakku after the invasion, the team refused to tell them about their failed invasion on the day of the black sun, when Bumi asked them.

Answer 1

Sokka specifically says this, emphasis mine:

So we're planning a smaller invasion. Just a ragtag team of our friends and allies from around the Earth Kingdom. We already ran into Pipsqueak and The Duke.

He also indicates their route on a map, describing how they've "been traveling west."

Note also that all of their named recruits come from places like Haru's Village, the Swamp, Gaoling and the Southern Air Temple, all locations in the south. It would appear that they committed to going south rather than going north.

The Mechanist was arguably the single most important person they got along the way, due to his creation of the various vehicles used in the invasion. I wouldn't be surprised if they planned their route specifically to get to him.

Answer 2

The Northern Tribe was being stretched thin. They probably couldn't afford to spare anyone. Couple that with the fact that they weren't in a convenient location near the Fire Nation, it would have made it even harder to send any support