Linda found a wash-out near one of the rose bushes, and by turning on Zone 3, it was clear that this was a leak. Digging down at this spot, it appears that a T-connector had broken -- not sure why -- and would need to be replaced.
This required cutting out the T-connector and the attached tubing and splicing back in, using straight connectors, a new T-connector.
Flushing the system and trying it out, showed another leak at another location, on the other side of the rose bush, where Linda had planted a milk-weed plant. That was just in a straight part of the tubing.
And fixing that one, and then testing the zone, showed a third leak, a bit further from the other two.
This repair was just cutting the leaking part of the tubing, and then inserting a straight connector into both ends. It leaks a bit, but that's what drip irrigation is supposed to do, so we won't worry too much about it.