The thin blue smoke (TBS) that you refer to is somewhat elusive. Use a quality wood, and not too much of it. A slow burn is what you are after. Clouds of billowing white or gray smoke should be avoided. A steady, slow expulsion of somewhat opaque light colored smoke is good; thin wispy smoke is better, similar to what comes off the end of a lit cigarette.
Pay attention to where you place your wood in the woodbox. Centered between the element rods may produce a longer smoke time than if placed directly above one of the rods. I say "may" because the type of wood used, and moisture content, and age of the wood can all have an effect on combustion and the amount of smoke produced. Also, air flow around the smoker for draw will have an effect.
I actually arrived at standing my wood chunk vertically to expose less wood to direct heat and get a longer and thinner smoke (as the wood burns, it will fall over). Whether or not this is better than laying in the wood horizontally at the beginning or not I truly cannot say. I had thick smoke one day so I removed the wood and started over with the chunk vertical. I liked the results and continue to do it to this day. It could have been the wood itself or its placement relevant to the heating rod.
You will find that your smoke will be more noticeable at the beginning, and taper off as time passes. I went through a lot of wood in an empty smoker getting a feel for it, wood quantity and placement,looking for TBS, which I rarely achieve. I get a nice clean stream of thin smoke now and haven't ruined a cut of pork in over a year. Wood is cheaper than meat, so take your time. And enjoy the smell while experimenting.