Yes, you got the wrong one. Don't worry about the voltage of the solenoid. The 6V isolated solenoid will work fine on 12V. It might actually just be easier to get a 6V isolated solenoid from a NewHolland dealer than track the right one down in the NAPA system... What you need is an isolated coil type solenoid that uses 3 posts and is triggered by ground... as opposed to one that is 3 pole and triggered by line voltage.
If you wish you could use the one you have... just use a cube relay to control the solenoid with the relay wired hot and it's control finding it's ground in the push switch.