Brom's Method Laterally Loaded Piles

It depends on your support conditions. The eccentricity is there to account for the moment and rotation at ground level.

If you've framed it with multiple piles and bracing or some other arrangement such that you can assume only shear loads at the top of pile cap then it will be top of pile cap to ground. If it's a moment frame, or single posts, or otherwise has a moment being applied to the pile then the e is such that the moment works out. So yeah, on a cantilevered sign it should be from ground to the point where the load actually works.

Additionally, in the past, when there's a moment from a source other than a purely cantilevered horizontal load I've taken e as whatever arm is necessary to create the groundline moment with the groundline shear (i.e. (M at groundline)/(V at groundline) = e. ) I don't actually have any literature that supports that, but it's always seemed to make rational sense. A moment is a moment.

I agree with with TLHS. 'e' should be determined by M/V.

TLHS - I worked out the statics years ago for the situation where you have an additional applied moment and it ends up being identical to how you approach it.