As to the DigiTrad version, most commonly sung in America these days, it is clear that he is saying farewell to the company on the spot ("I should rise and you should not"), but that he is also leaving town, and that right soon ("wish me one more day to stay"). Probably he has to get to bed betimes in order to get up & be off.

For me, most of the poetry is in the first stanza. There is a flash of malice in that "Alas" (if only I had had the guts to do the harm to my enemies instead!), followed by a flash of paradise (with the help of the booze & the company, he has gotten rid of all his shameful memories). If I were dictator, I would follow that up straight with the wonderful advice in Boswell's 3rd stanza: Your ain ills ay hae heart to bear, Anither's ay hae heart to feel. Fortitude & sympathy!

Thank God, the flame of conviviality is not quite yet out.