I just removed and replaced the tank for the first time. After re-connecting everything, I have a hose that doesn't appear to have a home. It's a shiny back hose that is attached to the top left of the carb. Thanks in advance.

There should be two of those vent hoses.  One comes off of each side of the carb.

I have those two tubes ducted into a .928" ID stainless tube running underneath the seat, exiting just above the rear tire.  About 4" from the aft end of the pipe is an electric igniter I pulled off the BBQ.

When I find I need some more power, I click the igniter, lighting the afterburner, so to speak.

There are a few problems, though.  
-- The first time I set it up, the carb exploded.  You shoulda' been there,... I must have looked like one of the balls of fire coming out of a roman candle.  Within a few days of checking out of the hospital, I repaired all the fire damage, and then installed a couple of one-way vapor valves acting as flame arrestors to fix that problem.
-- Another problem is the extra thrust doesn't last very long.  Just one loud KAPOW and that's pretty much it.  Sounds really cool though,.. everyone within 100 yds thinks I am shooting at them.  It is spectacular at night!

Maybe I should add a fuel pump and have it start pumping atomized fuel into the stainless tube.  Continuous afterburner, eh?
-- I could have it all controlled by timed relays and sensors.  
-- A low manifold pressure sensor could enable the whole system, then the igniter switch could close a relay to send 12v to the pump and to send 12v to a timed relay that would send nitrous to the afterburner .28 seconds after the fuel started flowing.



                                                                                                                       nah