How do I maintain the on value with a lightswitch-field as a plugin setting?
I believe you need to set the on value of your lightswitch field.

on: (settings.mailerShowInfo is defined) ? settings.mailerShowInfo : ""


So, the full settings of your twig code would be:

{{  forms.lightswitchField({
        label: "Show info in sidebar?"|t,
        id: 'mailerShowInfo',
        name: 'mailerShowInfo',
        value: settings.mailerShowInfo,
        required: true
        on: (settings.mailerShowInfo is defined) ? settings.mailerShowInfo : ""
    })
}}