Widget option not showing in Customizer

There are two things to try when a core feature isn’t working. First, try deactivating all the plugins and see whether that fixes the problem. If so, you know it’s a plugin conflict and you can try re-activating plugins one at a time to find out what causes the problem. If the problem is a plugin, you can contact the plugin developer about the problem or you can try to find a different plugin that does the same thing as the one that’s causing the problem.

If the problem isn’t a plugin, it might be in your theme code. Try switching temporarily to the default theme (Twenty Fifteen) and see whether that fixes the problem. If it does, it means that your theme needs to be updated for Customizer compatibility. In that case, contact the theme developer.