When you cook a turkey breast in an electric smoker, especially if it's a vertical electric water smoker, it'll need to be set up a little different that usual.
Turkey smokes well at a higher temperature than the ideal smoking temperature for beef briskets or pork shoulders. The reason is that commercially available turkeys and other poultry don't have the tough connective tissue and fat-laced meat like beef and pork do.
Connective tissues and fat require low and slow cooking in order to break down. It takes heat and time to accomplish.
In order to get the smoker temperature up, I use my vertical electric smoker with no water in the pan. So instead of heat energy being used to turn water into steam, it's all available to cook that turkey breast.
First, set the smoker up in a wind free location. Put up a windscreen of some sort if necessary. Blowing wind prevents just about any smoker from heating up to its maximum temperature, and with electric smokers (like the underpowered Brinkmann Gourmet electric smoker I have) it really causes problems.
Remove the water pan from its normal position, below the lower food rack. Put the rack back into position.
Place two pavers or red bricks on the lower rack, then place the empty water pan on top of the bricks. When not used filled with water to provide humidity to the smoker, the water pan makes a dandy container to catch drips.
Put the upper food rack into place. There should be plenty of room left above the top of the water pan for the rack to fit into place. If not, use thinner bricks.
Put the lid on the smoker and preheat it to its maximum temperature, or up to 300 degrees. The Brinkmann I have will only get up to 225 degrees on a warm, windless day. Like I said before, it's severely underpowered.
When up to temperature, place the brined and/or seasoned turkey breast on the center of the upper rack. Insert a remote thermometer probe into the center of one side of the breast. Carefully put the lid into position without damaging the probe lead.
Continue smoking the turkey in the electric smoker until its internal temperature reaches 164 degrees Fahrenheit. Turkey is safely done at 165 degrees, but the internal temperature will continue to rise a bit after removing it from the smoker from the residual heat. Now, remove it from the smoker and let it rest for 10 to 15 minutes before slicing to serve.