Given two dimensions:

Destroy any cell with only a left neighbour. Create any cell with only a bottom neighbour.

Start with a single cell: in the forward direction a vertical tower appears. In the reverse direction a horizontal row appears.

EDIT: I'm assuming that "neighbor" means a cell sharing an edge, but I realize that the Game of Life includes cells sharing a corner, so this probably isn't what you meant. Leaving it for... curiosity, I guess?

> In the reverse direction a horizontal row appears.

If you have a non-trivial row of live cells, then the cells immediately above that row will also become alive in the next (forward) instant. You end up with a row of N propagating upwards with a trail of rows of N-1.

I think your 1-cell example is actually a Garden of Eden in this rule -- there is no state that would produce it. The 1-cell itself isn't a still life, since as you note, it generates a vertical tower. Going backwards, a cell could only exist in the N+1'th state if it has a left neighbor in the N'th state; the only possible candidate for a predecessor would be the 2-cell row. But if we step this forward, we end up with three cells:

    OO
    O

The following picture has two predecessor states:

    _____
    _____
    __x__
    _____
    __x__

They are:

    _____
    _____
    __xx_
    _____
    __x__

and

    _____
    _____
    __xx_
    _____
    __xx_

Edit: Also, this has zero predecessors:

    _x
    xx