The thing that makes the *most* difference in bringing a faded Nikon rangefinder focus patch back to life is cleaning the diagonal surface of the half mirror prism. I've cleaned that surface on a Nikon SP and several Nikon S2s with faded focus patches, and after cleaning the focus patches went from almost unusable to almost or on par with a clean Nikon SP 2005.
It goes without saying that cleaning the front and side surfaces of the half mirror prism and the surfaces of the main prism will help, but that's only good for a 20% improvement. Cleaning the diagonal surface gives you the remaining 80% improvement. Below is a half mirror prism from a Nikon S2 rangefinder (removed from the camera for ease of cleaning). There is only a small gap between the prism and the metal casing so the trick is to slide some lens cleaning paper slightly dampened with lens cleaning fluid through that small gap. The Nikon pros at Kiitos Camera Repair in Tokyo use bamboo paper because its thin and rigid.
With the S3, you could also put a blue color filter (I used a B20 Fujifilm filter) on the main viewfinder window. It will make everything look blue through the finder, but the focus patch will stand out a lot more.
You don't need to take the rangefinder out of the camera to clean the diagonal surface of the half mirror prism. Instead, you can can access that diagonal surface by removing the front plate and small RF window, and then gently sliding dampened cleaning paper into/out of the above mentioned small gap. Repeating the cleaning six or so times should make a big difference. Just be careful not to get any damp lens cleaning paper stuck in there.
