Parking situation at Caltrain Tamien Station

I am considering using Caltrain to commute a couple of days a week from Tamien station. I understand parking is free at the lot, but the lot also looks relatively small per Google Street View.

Can anyone with current experience tell me if the lot gets full on weekdays?

For example, would I have to get there before a certain time in the morning to get a parking spot?

Are there alternative parking options if the lot is full?

According to Google Maps, it looks like there are two sides and two parking lots at this station (on the west and east side of Guadalupe Parkway; on Lelong St. and Lick Ave.). Which side should I be at if I want to take Caltrain northbound?