I crossed the border from Turkey to Georgia. The Turks are complicated! So this may help someone in the future on this border.
after the first checkpoint (passport/ID, vehicle registration check) you enter the area. Go to the left to the building and park there. Enter the building and go to the right side to the police counter and get your ‘leaving’ stamp on the white paper you’ve got while entering Turkey (not sure if you get this paper when entering with the passport, I’ve used my Swiss ID). Now go to the left side of the building to the customs (I took the right hand counter, it was not labeled) and they will type your info into the computer. Insist on your place in the line, the Turks will try to get in front of you!
now you can take your bike and go to the exit checkpoint. You may need to find a way between the trucks. They don’t have a line for incoming and outgoing, just one big chaos. I’ve been greeted on the checkpoint with my name before showing my ID (only motorcycle there), so they obviously check the computer.
After the exit there’s the Georgian part which is straightforward: go to the first booth, show your stuff without getting of the bike. Maybe the customs a few meters later want to have a look at your luggage, but it took only a minute.
it was about 20min on the Turkish part and 5min on the Georgian part. Don’t expect the Turks to know English…