Should I wrap at 150°F?

Only if the bark is already dark, which it usually is not that early. 150°F is the start of the stall, not a wrapping buzzer. Wait until the crust looks like you want to eat it. That is often closer to 160 or 170°F.

What if I never wrap?

That is a valid cook. A 12 to 15 pound packer at 225°F, unwrapped, is about 16 to 20 hours. You keep a drier bark and you must start the fire early enough. The calculator's wrap switch is the foil plan, which is shorter.

Does the wrap change the pull temperature?

No. You still pull around 203°F when the flat probes tender. Wrapping changes speed and bark. It does not make a 175°F brisket done.

When to wrap brisket | SimpleFood365

Wrap a brisket when the bark is dark and the center has been sitting in the stall, usually around 160 to 170°F. Wrapping at the first flat line on the graph, while the surface is still pale, steams off the crust. You can also choose not to wrap, if you started early enough for a 16 to 20 hour cook.

The decision, in order

The stall is evaporation. Wrapping is how you stop it. If you stop it before the brisket rub has set into a crust, the packet braises the outside and you get pot roast with pepper. Give the surface time. On many packers that lines up with the middle or late stall, around 160 to 170°F, not the moment the probe first touches 150°F. The cause of the pause is the brisket stall.

Then pick the material. Foil is the short plan: about 12 to 14 hours for a 12 to 15 pound packer at 225°F, and a softer bark. Pink butcher paper usually adds about 1 to 2 hours versus that foil window and keeps the crust drier. Both are compared on butcher paper vs foil. The brisket calculator uses the foil window when wrap is on. If you know you will use paper, start earlier than that foil clock.

Pros

Wrapping a set bark saves hours without erasing the crust completely, especially in paper.
Foil is the move when the flat has stalled and the serve time is not a suggestion.

Cons

An early wrap is the most common way to ruin bark that was about to be good.
Never wrapping means the long window. Hope is not a start time.

After it is wrapped

Leave the probe in the flat if the wrap will go around it. You still need brisket internal temp, around 203°F and a soft slide. A wireless probe that vanishes inside foil is a placement and radio problem, on Meater not connecting. A wired probe from meat thermometers for smoking is simpler once the packet is closed.

Rest after the pull, at least two hours, on how long to rest brisket. The wrap can stay on for that hold. If foil made the bark soft, open it for the last part of the rest so the surface can dry a little. The full cook around this decision is how to smoke a brisket.