If you're really worried about it, take the route over the Brennerpass. There'll be definitely something open on top of the pass at any hour.
For the rest, having ridden the Rando Imperator route, if you're quite slow stock up in Austria. Occasionally you'll find a pub in Austria open until midnight. On top of the Resia, take the main road. If you're at the Resia pass in late evening, don't bother with the bikepath but take the normal road. That's easy descending. You might find a bar open untill late.
The first ones will open fairly early as a lot of Italians enjoy an espresso before heading to work.