Have a watch nearby that shows seconds. A few minutes before your KQ starts, start watching your second clock and the KQ clock and memorize when your KQ clock turns the next minute and when your watch clock turns. Wait for your watch to be twenty or so seconds before your KQ clock ticks, and stare intensely at the status. Press down on your left mouse key and release at the right time. If you want to check if you are lagging or not, click the Participation key before the KQ is recruiting. How much you are lagging will affect how long it takes for the "cannot find KQ" message to show up. Move to a different place accordingly.
^ once I started doing that, I have NEVER missed a single KQ LMAO. It took me a long, looooooong time to think of it =w=