Thank you for the clear description of your P&S device.
You need to test your wires.
We are looking for the
Hot,
Neutral and
Load wires.
Your old switch has two wires.
One of these wires is the Hot (I suspect 100% that the wire that comes from the other wires that are twisted together is the Hot)
The other is Load
Separate the old switch wires and turn on power.
Use ordinary tester.
Test each wire to metal box and see if the box is grounded.
Tester will light up on Hot wire.
You can also test each of the old switch wires to the other wires in the box.
1) Hot: Once you determine the Hot wire, this wire will connect to the P&S device:
Hot connects to the brass screws on right side, just as you said ... and these screws are on opposite side from silver screw.
2) Load: The wire to Load connects to brass screw on top left, which is on same side of device as silver screw. This screw sits opposite the P&S switch.
The last wire is the Neutral.
Test your Hot wire to all other wires in the box.
When the tester lights up, that is the Neutral
3) Neutral connects to silver screw which will complete the circuit to the P&S receptacle.
http://waterheatertimer.org/How-to-select-right-wire-nut.html