I have left my car at the Sacramento Amtrak station for days at a time, but not WEEKS. I would suspect that this might be a problem. You pre-purchase a ticket from a machine and put it on your dashboard. IIRC, I don't think there is a two-week option available for purchase. Plus, over a period of two weeks, "regulars" will notice that it's always there, and after time it will gather dust and become an "Welcome" sign for burglars.

If it were me, I would ask the local hotels if I could park in their garage long-term. The Holiday Inn (walking distance from Amtrak) has an indoor garage that would be perfect for long-term. You might need to pay for the privilege, but at least you'll have your van still sitting on four wheels when you return.