Use Existing Wire
What I've done successfully is to to use one of the existing wires to pull a pull string through but there may be some problems one has to work around.Some of the OEM wires are taped together to form a wire harnes so trying to pull one of the conducters may not be possible. Secondly, the conduits are "split loom" which can allow a wire to exit out it's side. Thirdly, unless the pull wire and the pull string are taped together to create a smooth transition there may be some hangups, in which case one just has to back out and try another approach. Another problem is sometimes the wires are twisted, like three-strand rope, and it's hard to pull an individual wire through with the pull string attached as this causes a lot of friction.Once you've managed to get a pull string all the way through consider putting in another for future use after you've pulled your wire through.