A timed connection on the same platform in San Jose would probably be the most economical solution (or maybe even just Tamien, depends on space and passenger load). To be consequent, the San Jose/Tamien to Gilroy service could be done using a DMU.

Following the DMU idea, one possibility would be to have DMUs which could be MUed with the EMUs. In this case, it might even be possible to run through to San Francisco. On the other hand, that would require more DMUs than necessary, and tie them up for a long time outside of their intended operation field.

Coupling a diesel unit to an EMU for the extension to Gilroy would be feasible. It has been done in the past with no serious problems (TGV to some places in Normandy before the line got completely electrified). It may sound weird, but not too far off.

Dual power locomotives would be a possibility if (and only if) Caltrain would stay with loco-hauled trains. Otherwise, the loco hauled train would become a serious obstacle in a dense timetable. This also applies to running through with diesels.