Let's try to troubleshoot the issue during the start of a game:
The switch on G relay is a make/break switch (two switch stack), so if the coil is energized one switch will be closed and one will be open. Then the opposite is true when there is no power to the G relay coil. So, we'll need to know if the switch with the blue wire and orange wire on the G relay is open or closed when the machine goes through the reset process.
If we look at the schematic, it shows the switch with the blue wire and orange wire on the G relay is normally closed when the machine is powered off. And this is what we want - at the start of a game, the switch with the blue wire and orange wire on the G relay should be closed and there should be no power to the G relay coil. If you're saying there is no power to the G relay during the start of a game, then the switch with the blue wire and orange wire should be in the correct "closed" position.
If that switch is closed, you'll need to clean the switch again and adjust it. Sometimes you need to "scrub" the switch with a Flex stone or a paper finger nail file to get the switch contacts really clean. If you have a multi-meter, you can measure to see if you're getting any voltage at that switch...
I wouldn't recommend adding any wires to the machine, but you can always use some temporary jumper wires to get power to the G relay switch if needed for troubleshooting purposes...