2002 f1 50 disarm wire?

Relay is installed to convert + to - (+ signal coming from lock motor pink/black) and the factory remote works!  Thanks for the help in solving this issue.

My bypass is still giving me problems.  I called Omega tech help today and they recommended I get the ignition signal directly from the ignition 1 wire and to put the ground right to the chasis....so I did.  They also confirmed the RX and TX wires that I tapped into.  They mentioned sometimes you can try to reverse the RX and TX wires (I tried this with no success.)  The only other wire is the (-) ignition signal coming from the remote start (yellow/black) that goes to the brown wire on the bypass.  They also confirmed that 1 key programs it.  I've done all the above, and the theft light won't go solid during remote start unless I have the key in the ignition (meaning my bypass is not working.)  This is the final piece of the puzzle for my remote start to work.  Please reply with any ideas on getting my bypass to work.  Thanks! 

I did your above described test twice.  Once with the RX and TX wires hooked up per the installation manual, and once reversed per the mfg. suggestion.  No luck getting the bypass to work.

How do I test to make sure the brown wire on the bypass (- ground when running) is getting the proper signal from the remote start module? 

Any other ideas on why the bypass is not working?

Ground the brown wire of the bypass , then hit the remote starter see if it works. If so the ground status of the rermote start is not the right timing or is not working as it should.

Tonight I grounded the brown wire on the bypass, re-programmed it, and still nothing.  I also swapped the RX and TX, re-programmed, and nothing.  I'm assuming that I received a bad bypass module.  I'm going to request a replacement and hopefully this solves my problems.