In this short but very helpful answer @MikeH provides a link to this short item published in Nature:"...and farewell to the Pioneer Anomaly" which is well worth reading! It references a Physical Review Letter which can also be read via ArXiv for the specifics of the whole thing, including things like the screenshot below.
The Pioneer Anomaly is related to anisotropic thermal radiation. If the spacecraft is spin-stabilized, it's orientation is carefully maintained.
The Nature item (published in 2012) contains this forward-thinking paragraph:
"For decades, the anomaly remained. The Pioneers were realized to be uniquely sensitive to the decelerating force, cruising smoothly over huge distances because they were spin stabilized: other craft, including the Voyagers, were not, and their regular firing of thrusters to set or maintain course overwhelmed any sensitivity they might have had to the tiny Pioneer anomaly. There is some hope that NASA’s New Horizons mission, launched in 2006 and set to reach Pluto in 2015, might display a measurable anomalous deceleration, as it too is spin-stabilized for a chunk of its voyage; however, the design of the craft might result in some degree of unpredictable thermal-radiation pressure that would again overwhelm the effect."
How did that all work out? Did New Horizons "display a measurable anomalous deceleration" due to the same, now very well understood effect? And if so, was it during the spin-stabilized chuck of it's voyage?