2 pulse Positive to single negative out

I have an old 55t2T and cannot find the remotes.  The unit has a (-) Activation Input wire that I want to use to Remote Start the vehicle using the factory remote.  So I am wanting to convert the positive pulse from the Lock wire to a negative pulse and send the signal to the 552t upon 2 pulses.  Can this be done? A diagram or details would be much appreciated.  Thanks

Is this a correct diagram?

My company makes a module that will convert two positive pulses (within 1.5 seconds of each other) in to a (-) 100mA output.  The default pulse lasts ~10 seconds but it can be adjusted.  However, this route would be much more expensive (~$30) then going with a couple of relays and a few components.Kevin Pierson