To help support our community and customers during the outbreak of Coronavirus (COVID-19), LogMeIn is providing free Emergency Remote Work Kits for Health Care Providers, Educational Institutions, Municipalities, Non-Profit organizations, and current LogMeIn customers. For more information please visit https://www.gotomeeting.com/work-remote
Can you right-click GoToMeeting's orange flower icon in your system tray (the area next to your clock) and see if there is a log-out option available in that menu? If not, can you choose Preferences from that same location and see if the checkbox under Sign in is marked?
I believe I know what is happening; that sounds like your task bar, which has bigger icons that what your system tray should have. Check the corner where your clock is, and if you don't see an orange flower there right away, click the arrow and more icons should appear there.
If you'd prefer to talk to someone over the phone for help with this, please feel free to give our 24/7 support team a call at your earliest convenience.