How to find elements in a list satisfying different criteria

One approach goes like this:

First /@ GatherBy[list1, Last]

It turns out that GatherBy can be replaced by SplitBy.

You can also use SequenceReplace:

SequenceReplace[list1, {p : ({_, a_} ..)} :> First[{p}]]

{{3, 2}, {7, 4}, {12, 8}, {4, 10}}

This seems to work.

DeleteDuplicatesBy[list1, Last]

{{3, 2}, {7, 4}, {12, 8}, {4, 10}}