So using that, I would say that the longest line of sight in North America is from Mount Rainier, at 390km, looking North West into Canada: https://map.alltheviews.world/longest/-121.76853942871094_46...
That gives a longest in NZ of 365.3 km from Ruapehu, skirting past close by Tapuae-o-Uenuku (in the Inland Kaikoura Range) to a point on the Seaward Kaikoura Range near the peak of Manakau. Clicking on the actual Manakau peak also gives 365.3 km back to Ruapehu.
I can't seem to find a peak to get a reverse path back to Mt Ranier. Everything I try gets stuck in the Olympic Peninsular. (I was there once ... 1998 or so ... a place called Hurricane Ridge IIRC)
So this is the NZ longest line right https://map.alltheviews.world/longest/173.61386108398438_-42...
One thing to note about finding reverse lines, is that they're not truly mathematically identical because the observer always has a height of 1.65m and the destination is always some point at the surface, therefore 0.0m. It doesn't always make a difference, but it sometimes can.
Anyone with expertise want to comment?
Mountains can rise higher near equator because you have the least gravity there. The whole Earth bulges along the equator. But I don't think it's measurable.
So that large lines of sight are near the equator on a north south axis (or symmetrically south north) is crazy because the high rates of curvature in that direction at those latitudes should give the shortest distance to the horizon on earth, making those lines of sight even that much more impressive!
It is not about highest point from centre of Earth. That's is related to equatorial bulge but irrelevant to the discussion.