I read on http://www.caltrain.com/riderinfo/Parking.html (mirror):
Parking is available for Caltrain customers at most Caltrain stations.
How does Caltrain check whether cars parked at Caltrain stations belong to Caltrain customers?
From https://www.parkme.com/en-gb/lot/187135/mountain-view-station-mountain-view-ca, found by Nate Eldredge: "Permit Parking for Caltrain Patrons ONLY".