I'm trying to imagine what there was worth invading east of San Diego. Even modern El Centro does not look like much.
In 1916, there was nothing much inland at all, just desert. I suppose he could make his way up through what is today the Inland Empire toward the Cajon Pass, flanking LA and San Diego to the east, but there wouldn't be much of value there unless he got far enough north to disrupt rail lines out of LA. I imagine that would be put down by the US in a hurry and the danger of going that far north is that you get cut off when US forces are reinforced. At best, he could try for some of the smaller border towns but they wouldn't have a whole lot of value. In the era before freeways and good paved secondary roads, this is very inhospitable terrain for the most part and a very inhospitable climate much of the year. One thing that does occur to me is that if this is done, you could see an even greater hostility toward Mexican immigration through the early part of the 20th Century. Make it bad enough and some of the early Mexican settlers who had been in California for a while might be pressured into Anglicizing their names and scrubbing the family tree of Mexican roots. Similarly, there might be moves to change or Anglicize place names, e.g. Santa Monica becomes St. Monica, Los Angeles becomes The Angels, San Francisco becomes St. Francis, Mount San Jacinto becomes Mount St. Hyacinth and so forth.