Remote Start not working in Cold Weather

I installed an Autopage RST-2053AL in my girlfriend's 1996 Plymouth Breeze 2.0L 4Cyl about 2 years ago. I did not opt to hook up the tach wire when I first installed it since it was warm outside and the default settings (voltage start, 0.6 sec crank time) worked perfectly. That winter, the unit would not start the car when it got cold out (Whats the point of remote start when it doesn't work in the cold?). When the start button was pressed: The parking lights would flash,the doors would lock, the ignition would turn on, and the starter would make a short grunt then stop. Nothing happened after: no fault codes, it appeared as if the module thought the engine was running. Right away I suspected that the crank time could be increased. I increased it a little at a time all the way up to its maximum (3 sec). This had absolutely no effect on the crank time, not even a longer grunt from the starter. Next I decided to hook up the tach wire and try the "RPM Start" mode. When I press the remote start button in this mode I get a single flash from the parking lights ("Diagnostic Parking Lights" section of manual indicates that "1 Flash ---- RPM fail") then nothing, no ignition, no door lock, no start attempt. I hooked up the green tach wire of the alarm module to the black with grey stripe at the coil pack. Is there something I am overlooking?? Is there a tach programming mode for this module to learn the tach signal?? Winter is here again and I would really like to get this thing working before my girlfriend looses all faith in my abilities and dumps me.

Oh, and another thing. She claims that the cruise control only works intermittently since I installed the alarm. I thought it might have something to do with the brake switch wire to the alarm. I unhooked the wire and the cruise control still only worked intermittently. Could this have anything to do with the remote start problem??

I am out of ideas. Any help would be greatly appreciated. Thanks in advance.

Thanks for the reply, but It didn't work.  I tried holding down the valet button but nothing happened.  Niether the Install Manual nor the Operation Manual say anything about learning the tach signal.  The only adjustment listed for RPM start is 75% / 90% /110% RPM Value.  Percent of what value Im not sure, but I have tried all 3.  I measured the tach signal and at idle (about 750 RPM) my DMM measured about 14 VDC, 5.5 VAC, @300 HZ.  The VAC and HZ increase with the RPM.  Seems to me like this would be a good tach signal (although its only 2 cylinders - one side of the coil pack).  Any other suggestions?

Check the output voltage of the crank wire during a remote start.

Does it have voltage for a second, minute, hour, day, week?

Also check the input voltage of the alarm during a remote start.

Does it have voltage for a second, minute, hour, day, week? Does the voltage drop during a remote start? Have you checked and rechecked all the connections? Did you solder the connection or use crimps?