Revealing mistake: During the car chase with the railway train wheels, when some of the cars get destroyed and flipped, you can see flame and smoke from the bottoms of the flipped cars where the cannons fired to flip them.
Revealing mistake: During the truck chase and the train wheels being offloaded into the path of the pursuing cars, on the car that gets hit after the hummer we can see the metal canister used to roll the car.
Chosen answer: It appears to be some sort of cable - it can be seen leading to the bracelet in the shot from above the bed immediately prior to the one where Lincoln unplugs it. Exactly what it does is never revealed, but it seems likely to be some sort of monitoring system, keeping an eye on Lincoln's health through sensors in the bracelet.
Tailkinker ★