What you're talking about is generically called autotracing in centerline mode. Most autotrace programs can either try to trace all the way around the areas of dark pixels (outline tracing), or try to trace along the middles of areas of dark pixels (centerline tracing).
In Illustrator's autotrace settings, for centerline mode, you turn off the tracing of outlines (fills) and turn on the tracing of centerlines (strokes). That's the basic setting. From there, you try to adjust the various threshold settings to get as close to what you want as you can.
When Illustrator's autotrace feature is set to try to trace centerlines, it also tries to set the vector path stroke weights to approximate the thicknesses of what it interprets as a stroke. So after the autotracing is done, you can expand it and then globally set the stroke weight to a uniform value.
Beyond that, no one can really advise you more specifically without seeing the specific image involved. Every image is different.
Generally speaking, autotracing is crap. It's an amateurish workaround to avoid doing what should really be done: Trace the paths manually with the drawing tools.
I appreciate the input and insights into the program.
You've pretty much answered what I needed and I think it will allow me to finish this first project for the client.
I agree that it will probably look/be a much more professional piece of work if I were to take the time to trace the full drawing, however since I'm a full blown beginner and using a mbpro and mouse, tracing the image is beyond frustrating. Hoping to eventually have a full copy of the program and a good workspace with a pad and pencil to get into the nitty gritty
Thanks for your help have a great weekend and I'll post back possibly with an image if I need more help!