This mission becomes available if you agreed to help Captain Monroe during Archaeology for Beginners and is a simple mission to Gold Medal provided you skip cutscenes. It’s a timed mission and you only have 5 minutes to do it however there’s no shooting so it’s a mission ideal for a replay.
Mount up and follow Captain Monroe to the lookout point as he explains the mission. You’re to sneak onto the back of the army wagon and take the vaccine without causing any trouble. Once the cutscene ends (or you skip it), quickly mount up again and head down the hill to the south, waiting for the wagon to pass you.
Gallop up to the side of it but still towards the back of the wagon and wait for the prompt to jump to the wagon. Once on board, search the grey lockbox to your left and take the vaccine before jumping off the back. You now need to gallop back to Wapiti as fast as possible and it’s quite a journey from here so you can’t afford to take any detours or stop once. Once you reach the reservation, dismount and head over to the tent to find Captain Monroe and end the mission.