Batt (+) connects directly to the Cathode (banded end) of D1 which also connects directly to one end of the Relay's Coil lead, there should be Batt (+) volts at this point.
The other end of the relay coil is connected to the collector of Q4. When no motion is detected, the volts here should also be Batt (+) but when motion is detected, this volts should go to near zero, which will pull in the relay......the volts at D1 Cathode should remain at Batt (+) at all times.
Batt (-) connects to L3 (the white wire was (is) connected at this location
I think you need to double check the wiring you guys did.
At idol (no motion detected and don't forget the sensor takes 20 or 30 sec's to warmup and will be triggered then) You should be getting batt (+) volts on both ends of the relay coil.
I stick one of those Auz Pencil Erasers you can buy and stick on the end of a pencil (triagular shaped) over the sensor when I want it to not trigger.
Once it's triggered, the volts at the D1 Anode end (not banded end) should go from Batt (+) to near zero (but I havent measured it) and the relay contacts get closed. If you are getting 5.97 volts then 12 - 5.97 = about 6 volts which means the relay coil needs to be in that neighbor hood, are you using a relay whos coil is 12 volts or 9 volts, 6 volts probably won't even pull in a 9 volt relay tho?