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We present a two-epoch Hubble Space Telescope study of NGC 2071 IR highlighting HOPS 361-C, a protostar producing an arced 0.2 parsec-scale jet. The proper motions for the brightest knots decrease from 350 to 100 km s ^−1 with increasing distance from the source. The [Fe ii ] and Pa β emission line intensity ratio gives a velocity jump through each knot of 40–50 km s ^−1 . A new [O i ] 63 μ m spectrum, taken with the German REciever for Astronomy at Terahertz frequencies instrument aboard Stratospheric Observatory for Infrared Astronomy, shows a low line-of-sight velocity indicative of high jet inclination. Proper motions and jump velocities then estimate 3D flow speed for knots. Subsequently, we model knot positions and speeds with a precessing jet that decelerates. The measurements are matched with a precession period of 1000–3000 yr and half opening angle of 15°. The [Fe ii ] 1.26-to-1.64 μ m line intensity ratio determines visual extinction to each knot from 5 to 30 mag. Relative to ∼14 mag of extinction through the cloud from C ^18 O emission maps, the jet is embedded at a 1/5–4/5 fractional cloud depth. Our model suggests the jet is dissipated over a 0.2 pc arc. This short distance may result from the jet sweeping through a wide angle, allowing the cloud time to fill cavities opened by the jet. Precessing jets contrast with nearly unidirectional protostellar jets that puncture host clouds and can propagate significantly farther.