Lawn irrigation system

Really?  I had a guy 'water witch' to identify location of sewer lines on my previous property.  He swore up and down that the location he marked was correct, (one lateral drop coming straight up the middle of the driveway).  I knew otherwise, and sent him back to city hall to pull the 'as builts', and come back with a tape measure.  He was 50 feet south of the FIRST, and 56 feet south of the SECOND.  I advised him to set aside the idiocy, and use legally-mandated methods.

About six weeks later, he did same thing, and the backhoe ignited after striking a 13kv underground line that HE identified 40 feet elsewhere. Operator was killed, lawsuit followed, "witcher's" failure history was reviewed, at which point he was fired, sued, and is now in jail.  The short story: there's proper instruments for doing locates, use them, or don't do it at all.

If you want to find those boxes and heads, apply compressed air or water, that's what the irrigation professionals do.  If you need to find the plastic lines, once you've found the HEADS, tie a 'stringmouse' to the end of some jet-line, suck it through with a vacuum, tie a piece of 20ga wire to the jet-line, pull it through, connect an RF locator transmitter to the wire, push the ground stake in, set it to 80khz, low power, turn the receiver on, set it to mid-sensitivity, and carry your marking paint... you'll have it all mapped out in no time.

The Ditch Witch 75T/75R kit is my favorite... it has a three-dimensional diversity array which will identify the distance to right or left, and depth of the locate, and it's usually within an inch or so.  I've used a fishtape shoved down a sewer pipe, and set to 5khz, got an accurate locate down 5 feet...  direct connected a common frostless steel yard hydrant, and managed a good locate at 7ft (also 5khz) for a distance of 45ft.  Many locator units can also detect electromagnetic anomalies along the path... i.e. if you're traversing an area following your transmitter's target line, and there's an underground electrical cable carrying current, the receiver will detect and alert of that WHILE following the injector's signal... very handy when you're working on an unknown property with lots of 'history'.

Does it have to be SOLID? 

Okay, so MOST sprinkler heads are somewhat 'removable' for service... meaning, you can push-twist-pull or unthread them from the base... Find yours, look for any brand marking, then look 'em up on the net to see if you can find out how they come apart for service.  Once apart, make a fitting using whatever you can, to connect a garden hose to the sprinkler base... or if not, dig around the sprinkler head, find the feeder tube, disconnect the base from the tube, and connect a garden hose...  apply water pressure to it, then look for where it's coming up in the yard... there's PROBABLY a distribution block buried in a well-box under the lawn a few inches.

Re. your controls question, most sprinklers now run solenoid valves at the distribution block (which can be in the yard, or in the basement or crawl space of the house, or in a shed)... sometimes, it was controlled by a 'passive' gadget that had a little flowmeter-type paddle valve that spun as the inflow passes, after so many rotations, it switches to the next circuit.

re: Still have not discovered where the system taps in the city water supply.

as long as it's BEFORE the meter don't worry, be happy !!!