When you cut up a 'plug n play' tail where does the 'white' wire go to?

where does it go on the track? I imagine the white wire might actually be some sort of serial control or something for a legacy/tmcc signal but I don't actually know for certain. Does it work without it?

For this particular accessory, white has no function (the pigtail section of the manual doesn't say to do anything with white, right?  Therefore, by extension, there is nothing to do with white if you cut off the end on the accessory side either.). 

White is used as an activation for other units such as the Burning Switch Tower or Control Tower.  Each come with activation switches, but also have some function you generally would want on all the time (like the light in the Control Tower).

Look at the hook up instructions (not just for this, but for any accessory where this topic comes up).  There are instructions for how to hook up to TMCC controller items (SC-2, etc - these replace any included activation button, generally) that you can derive what is needed for hookup. You will pretty much always see post of the transformer hooked up to one color wire, and the other post of the transformer is then hooked up to the TMCC controller.  The wires from the accessory are then hooked up to the "posts" on the controller that makes the contact when you hit Aux1 (momentary activation) or Aux2 (on/off toggle activation).

The work house simply syncs up because we are programming it with the same engine ID as the crane itself (the same way 2 TMCC/Legacy engines will both respond if they have the same ID #).

In another thread someone asked about how to wire the control tower without the button, which is a similar question with a similar answer. 

It seems based on your research (cutting off the connector ) that Lionel did (at least for this accessory  - hopefully will continue) maintain the wiring color code on the accessory side of things. 

While that is of course good practice, I can easily see it coming up one day where they do not.  A question may be posted to the forum says "I clipped off the connector and now I have green, blue and orange  wires - now what do I do?". 

-Dave

The white wire is not used or needed when you cut off the end  just attach the red and black wires directly to the track or to your transformer as per the instructional booklet provided by Lionel. Red goes to middle rail and black goes to outside rail.

-Pete