What he said.
If you've only installed a Viper before, you probably remember, just as you said, that the unit has a green wire and a purple. You cut the car's starter wire and connected the green and purple to each half.
That's because the Viper (thankfully) already has the starter kill relay built in---when the alarm is armed, and you (or a car theif) turns the key to Start, power goes into the green wire, but the kill feature doesn't allow any power to come out on the purple wire....and therefore the car doesn't start.
The Autopage unit doesn't have a built in starter kill; it uses an external relay. The relay (and its plug-in wire harness) might be shipped loose in the box, or might be pre-wired to some other part of the alarm to save you a litle time.
Like 1xle said, you could choose to simply not connect the starter kill feature at all (your car does have an immobilizer key from the factory), or connect it as shown in the diagram.
The diagram shows you cutting the car's factory starter wire in half, then connecting each half to the appropriate wires from the relay...........and then it shows you connecting the purple wire a little further "downstream" along the car's factory starter wire.
They drew the diagram that way just for clarity. Most installers would take the "output" side of the starter kill relay, the purple wire from the remote starter, and the "downstream" side of the car's factory starter wire.....and connect all THREE wires together at the same time. Just makes the job a little neater and quicker....but that's up to you.
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As far as the neutral safety switch shown in the diagram:
1. You're already (I assume) making your connections under the driver's dashboard, in the harness that comes from the steering column.....you can visually see that there are no other devices in between your connections and the car's keyswitch.
2. Because of that, you KNOW that the Toyota's neutral safety switch is somewhere "downstream" from your connections, just as shown in the diagram. Maybe the Toyota neutral switch is at the shifter, maybe it's under the hood near the car's starter motor.........you really don't have to know or care where it is, since you already know that you're doing your work "upstream" from the switch as you're supposed to.
3. Because of #1 and #2 above, you can rest assured that you're doing this part of the job correctly, and that after the install is done, you can do the test described in the install guide if you'd like. The remote starter will not crank the car if the car is in gear.
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Second starter wire:
Yes, you're right. Use the unit's negative second starter output to drive a relay, to trigger the car's second (small gray) starter wire. I'd guess that the Autopage install guide probably even includes a relay diagram for you.
Some installers shortcut by simply jumping the two Toyota starter wires together and treating them as one, but that's contrary to the way the car was designed.....Toyota must have used two separate circuits for a reason. It's just as well that you're starting your installation with good habits!
Also, to perform the starter kill function, to keep the car from being stolen, you only have to interrupt one of the Toyota's starter wires with your relay. I always interrupt the bigger wire just so my installations are all consistent, but you can choose either wire you want.
Again, you don't need two starter kill relays, and you don't need to interrupt both wires. Interrupting either wire will prevent the car froom starting.