Gosse's Siding opened right here in May 1908, 28 years after the rail line had been installed. Gosse ran a quarry here but there is a newspaper advert in 1909 that said he had finished his contracts and was selling his draught horses and plant (Every horse is a worker and staunch, not a waster amongst them), suggesting that he used the siding for less than a year. Sometime around 1918 or 1919 it was renamed to Andrews Siding. Perhaps the business it supported had been renamed. But in 1933 the stop was closed.
By 1938 a community had sprung up around here and Pitcaithly's station building was moved from 600m north to right here to better serve them. The stop was re-opened for passenger traffic only and renamed to simply Andrews. None of my references give the reason for the station's name. There is a suggestion that it was named after J.W. Andrews who was the first Mayor of Lower Hutt. However John was 27 at the time Andrews Siding was named, and didn't achieve mayoralty till 15 years later. Possible, but I think unlikely. More likely it was named after a business here. Perhaps John's parents?
Andrews was finally closed in February of 1954, when the rails through here were pulled up. It was never more than a small shelter shed with no platform. None-the-less business seemed to grow and to warrant someone stationed there in 1915 to sell discounted day return tickets for the excusion trains celebrating the Wellington Province anniversary.
Now, of course, the motorway runs over where the rail line was and there is no evidence of the station or the line anywhere.

Andrews, 1953
References:
"Railway Directory", Hutt Valley Independent, 2 September 1911
Auctioneer's notice, Evening Post, 23 January 1909, page 16
Scoble, J: "Names and Opening and Closing Dates of Railway Stations", published by the Rail Heritage Trust of New Zealand, 2010.
Parsons, D: "Wellington's Railways Colonial Steam to Matangi", published by the New Zealand Railway & Locomotive Society, 2010