no
In your drawing;
#1 from the Trans connector goes only to one of the switchs, say to the upper switch; and from
#3 only to the other switch, say the lower switch.
Both of the still unconnected snap switch terminals, would then go to any chassis ground
The yellow wire in the center at #2, is the 12v supply and it should go to an ignition circuit that is hot in Run and turns off with the Ignition switch.
I assume the box in the upper left is a relay, But it appears not to be connected correctly. But it's hard to tell by the identifiying letters.Just make sure it is a fused source that turns on and off with the ignition switch.