2001 ford escape remote start

I would have to see the motor to help you with the tach, so i'm no help on that. On the doorlocks, i would use the WHITE/ violet and blue/green wires for lock and unlock.(set to double pulse unlock).

When doing the tach signal you can always use fuel injector wires.  Its usually a two pin plug.  For example, on a an 2005 acura TL you would take off the engine cover and it will show these type of plugs across.  They would have  one wire thats the same and the other would be a different color.  The different color would be the signal.  To check for the signal you can use your multimeter and change it to AC and tap that wire.  You would see the wire with a pulse on the meter.  If you shut down the vehicle then the pulse is gone and or if you rev the vehicle it will pulse higher.  In regards to the locks, make sure you use relays for the lock and unlock wires.  One of them is like you mentioned the 1k ohm resistor and the other is not.  you must use relays though, do not connect direct.  The factory alarm disarm is blue/lt green at the GEM.  I dont know if it will unlock the doors.  Direct Techs doesnt mention anything about this other then that the factory arm wire will also lock doors.  You can also disconect the lock wire with the 1k ohm and just have the unlock wire connected.  If it unlocks then you can connect your lock wire to the factory arm wire and leave the unlock wire on the pink/white wire.