So to recap
orange equals 12 volts
White equals ground
Gray and purple equal coil wires
Looks like you got it.
So Orange and white to the center terminal on the SPDT switch
gray and purple to the top or bottom and purple and gray to the other end.
(Note the reverse of colors.)
It's a good system. Careful of the 5 amp fuse.
NOTE if you have a box somewhere labeled "Intelletec Battery Control" the Solenoids are inside that behind the fuse panel There are also Test points on the fuse panel Left side about 1/3 the way down the test points consist of a Tab and a Pad.. Using a test light clip on the tab and touch the pad.. Operating the switch EITEHR WAY should cause light to bright.. Volt meter will show + one way and - the other.
Been there.. Done that. As they say.