Since I live in the area, I have a bit of additional information.
First of all, the road where you park is *a* frontage road (meaning, a road that parallels the freeway), but the actual name is Old Highway 80. It’s called “old” because I-8 was built to replace it. The former Highway 80 lost its official designation at that time, but survives as a street name. The former highway 80 extended from San Diego to Arizona (and I believe it went on further all the way to the East Coast). Lots of history along the whole old Highway 80!
Secondly, the fences you describe have nothing to do with the border. They are simply the fences around the freeway right-of-way; you find them around all the freeways in San Diego (and probably elsewhere). Border Patrol isn’t so much looking for people coming from Mexico (there aren’t any; the border is close to 20 miles away); they are looking for people, mostly Americans, trying to bypass the Border Patrol checkpoint on the freeway – those tend to be smugglers. Caution: border patrol vehicles are sometimes speeding and have caused some serious accidents.
It is sad to say this, but if you look non-Caucasian, bring identification. You will have to pass through the border patrol checkpoint on the way back. Also, the checkpoint sometimes uses drug-sniffing dogs, so don’t even think about bringing illegal substances (even if they are legal in California – the checkpoint follows federal law).
Third, as a bit of trivia, there actually is a ghost town about two miles away right on Old Highway 80 (it is currently for sale, as of March 2017). You can still see remnants of two buildings, and there are foundations of more (there are more ghost towns in the area).
Do not approach the buildings – they are on private property.
The name of the ghost town is Buckman Springs. If you stop at the Buckman Springs freeway rest stop, you can see a plaque describing some of the history. Amos Buckman and his daughter operated a water bottling plant. There was a spring with very mineral-rich water nearby.
If you follow Kitchen Creek to the end, it merges with Cottonwood Creek. Cottonwood Creek, in turn, runs into Mexico and eventually becomes the Tijuana River.