What color should I use to paint the wooden gable?

Console, gray, that would work. Available everywhere. At least two coats.

Take a look at the country house paint from OSMO.

It's not exactly cheap, but it spreads really well and covers nicely.
I would also paint at least twice to ensure an even coverage.

We painted our entire carport + privacy walls, bench, and shed with the country house paint in stone gray and are very satisfied because the rainwater beads off nicely, but the wood can still breathe since the paint is open-pored.