Ok, let me back up a bit then.
The line that supplies water from the supply to a Zone Valve or manifold is called a mainline. The line that supplies water to sprinkler heads from the Zone Valve is called a Lateral. Branches are typically just small, flexible pieces of pipe that connect the actual sprinkler head to the Lateral. Sometimes/often, these are arranged in an assembly called a swing joint.
Many systems have an additional valve, electrically controlled, before actual zone valve called a Master Valve. The valve you mention out by your sidewalk sounds like it's just a manual Shutoff/Service Valve. The easiest way to see if you have a Master is to check and see if there is wiring for it present at your controller. If there are no wires present for a Master Valve, skip the rest of this paragraph. A Master Valve is open anytime your system is watering a Zone. If a Zone Valve was leaking for the area in question, it would do so whenever the system is running, even if the problem Zone hasn't run yet. So no need to get wet, just run 1 or 2 Zones that are NOT the Zone that leaks and observe whether or not you get water at the heads in question. You could also manually open the master valve (the method of doing so varies somewhat from brand to brand) and not run any zones. Leave it open for an hour or two and see what happens.
If it IS a zone valve leaking, then it would normally present itself at the first one or two heads along the lateral unless others are significantly lower or they have certain features like a built-in check valve that cause the trickle of water to leak from other heads first. That's why I asked about the brands and type of heads you have, to see if we uncover any "ah-ha" moments for strange behavior that otherwise defies the laws of physics.
If it's wet out there ALL the time, even if the system has not run for a few days, and you don't have a master valve in the system, confirm that it is the zone valve leaking by shutting off your service valve for a couple days.
It's also possible that you have a problem at the heads themselves. Loose connection, cracked bodies, damaged pipe, etc. This would be the case if the water only shows up while that zone is running or has recently run.
The good news is that spray heads are pretty universal, and dirt (haha) cheap to replace. You may not even have to unscrew the head from the branch piping if the bodies are compatible as many of the common brands are, just unscrew the guts from the outer body and screw the new one on. Even if you elect to replace the entire sprinkler head, you could do it after the zone has been off for a few days (it does rain in SoCal on occasion right?) or just dig a little next to the head so that any water that comes out of the pipe has somewhere to go instead of collapsing the hole. You don't need to dig out a huge hole, just couple inches under the base of the sprinkler and a hands width or so to the side will do fine. You can use a small potting/garden spade even. I have an
irrigation shovel that has a full-size handle and the spade is only 4" wide. But I do this kind of stuff on semi-frequent occasion and love accumulating tools.