Hi Doug,
The thick white wire, blue electrolytic capacitor, black diode on the blue cap, and wires attached to the blue cap are an untidy modification to replace the original, green 'tin box' capacitor, shown in your pic. The original wiring of the transmitter to the slave should appear as in the pic's referred to in the hints / tips link provided. In the link pic's, the green capacitor and bobbin coil are mounted in a different position in the transmitter case.
It would not be advisable to attempt to re-use the green capacitor in your set up.
The whole arrangement of the transmitter and slave impulse movement should be in series. Ie the transmitter armature contact in series with the transmitter coils which in turn are in series with the slave movement coil. The power supply is applied at each 'end' of this series arrangement.
For a 12 volt DC power supply the arrangement would need an additional resistance of 24 ohms at 3 watts or more included in the series circuit, assuming the transmitter and save coils are the usual values of 30 ohms (15 + 15) and 4 ohms respectively. Your transmitter should have a 'Rheostat' fitted in the transmitter case to introduce this additional resistance. As
The polarity of the DC supply should not be important, but would be critical where dioed and/or electro cap's are used as spark suppression across the armature contact.
Hope this helps,