Up in Santa Clarita, CA (about 35 miles North). I just wasn't sure if it is normal to have taxi stands, any shuttle van services, etc. Are there rental counters there?
Just realized that if you say you are arriving at LAUS around 9 p.m., you will be on the Coast Starlight 11.
If this is a correct surmisal on my part, then you should get off the train one station before LAUS, at Burbank-Bob Hope Airport. The Airport is literally across the street from the stop, and there is a shuttle to the terminal.
At the airport, you will be able to get a shuttle to Santa Clarita. There are several companies which you can find on the Internet or by going to the airport's website on ground transportation. Burbank Airport is the closest one in the LA area to Santa Clarita. Your hotel also should probably have good information on shuttles from Burbank.
If you rent a car, you probably would find open counters at the airport even on News Years Day night.
Good luck.