The way the circuit is designed is really quite clever.
When you first turn on the key the alarm should sound because it is getting it's ground from the low impedance of the non operating fuel lift pump. When you press the start button and the engine turns, the oil pressure switch closes when the oil pressure becomes 5 psi or greater. Current is now delivered from the bat. through the key switch to the fuel pump. The closure of the oil pressure switch also places +12 volts on either side of the alarm silencing it. The same circuit also controls the lo-oil light. If the oil pressure switch is not connected, than the alarm will continue to sound even after the engine has started. The engine will run without the fuel pump operational if your fuel tank is 3/4 or more full because of gravity feed, so beware.
The bottom line is it should sound when the key is on and the engine is not running. Why you are getting a screech sound instead of a normal alarm sound is most likely due to low voltage, check all your connections. Also check the shovel connector at the fuel lift pump. If it is corroded the alarm circuit will not sound correctly or weak because it is not sinking the current thought the fuel pump.
A water light? My control panel has a gauge for water temp.