Tinkering is a goal which unlocks the tinkering task at the campsite. Since tinkering allows followers to research technologies which give you advantage exploring the map and allows to craft items which can give an advantage in combat, it's adviced to do finish this right after finishing Jungle Drums. The quest is immediately added to the goals after finishing the governors first mission.
After speaking to the governor, head towards the market of Santo Domingo and select the options to look for Umberto. After spending quite some time to find him, he takes you to some stalls which sell junk to make some barricades and then teaches the party to make some barricades. He will give you three barricades which you can use during the battle.