This song is about leaving rather than dying

I'm not at all sure about that. It always seems to me a very appropriate song to sing if you knew you were were being hanged in the morning, and I can quite imagine it originating in such a setting. Parties in such circumstances were quite common among highwaymen and such, I believe. (cf The Night before Larry was stretched - though I'm not suggesting that one.)

There's also the other version of the Parting Glass - Here's a Health to the Company.

It's worth remembering that a lot of Irish songs about parting originated in circumstances where parting was expected to be as final as death - hence the tradition of the American Wake.