In the schematic, T2 has collector and emitter reversed. Emitter should go to positive supply rail. It looks like T2 (PNP) is supposed to provide on/off hysteresis but I haven't done the math.
Drat! The error in my attached schematic is totally my fault. Floobydust is correct to say that its the B192 kit, and the scehamtic there is correct, but doesn't have component values. I created my own schematic to make it easier to debug and discuss here.
Both transistors are connected the correct way on the actual PCB, the same as the PCB markings and the photos on the URLs that floobydust posted.
You should not have 4V across R1. That means T1 E-B junction is not there, so T1 is likely installed wrong which could make T2 stay on all the time like you are seeing.
Interesting. If T1 was working correctly what would the expected voltage by across R4? The transistor is currently installed the right way around, but I believe there were some issues with the transistor installation to begin with, and they were removed and redone. It's possible they were either killed with heat from the removal process, or perhaps blown when they were installed the wrong way...
R4 adds hysteresis to the circuit, when T2 is turned on due to water present R4 helps provide a tiny extra base-drive to turn on T1 harder for sharper switching action.
That makes sense. It's almost like adding a bit of positive feedback, right? I imagine that the value of R4 has to be chosen correctly to prevent T1 from being turned on permanently?
I kinda don't like these circuits because they have DC at the electrodes which causes corrosion, and it is sensitive if the water tank is at earth-ground potential compared to the 9V power source. It makes them malfunction when powered off a wall-wart vs 9V battery.
Thanks for the heads up. Thankfuly this is just a fun silly project, it won't actually be used 'in anger'.