"Saturdays also still had several actual commuter trains in addition to the base schedule".

The pre-Caltrain SP schedule only had one Saturday train that made less than all of the local stops. That was southbound train 126, which was a daily train with limited stops. The San Francisco-Monterey Del Monte was combined with that one weekday rush hour train around 1960, so 126 became a daily train on the same schedule leaving at 4:50pm.

I don't think SP cared about having a Saturday and Sunday limited stops train. They just never bothered to change the schedule after the Del Monte was discontinued on May 1, 1971. So limited stop train 126 remained daily until Cal Train changed the schedule.