If your Honda is the same age as mine, and it sounds like it is, if you take the side cover off, there is a screw on the bottom of the carb that will drain the carb completely. The new fuel shut offs are nearly worthless in my opinion. Running an engine until it quits does not empty the carb of gas, it just gets the gas level low enough to no longer run, then the remaining gas can sit there and varnish things up.
Either drain the carb using the built in drain, or run it monthly to get fresh gas in the carb. I guess I don't see a need to do both. I run mine monthly, and always use Seafoam in premium gas, and that is all that my Hondas ever see. While I am kind of a fan (not a huge fan, but that is a different post) of ethanol, it isn't used in any of my small engines.
