"Leave on" vs "leave"
In my opinion, as a Brit who has lived in the US for 20+ years, British English would always include the "on", whereas it is optional in American usage. In both cases there is an unstated object in the sentence, such as "here" or "home".
I think the answer depends on your intended audience: if they are expecting American English you can leave out the "on", but if there are Brits or people expecting British usage, you should probably include it.