You are essentially correct to assume that the precession is sometimes backwards as well. The frequently quoted value of 531"/cy is only the long term net average. In reality there is a considerable oscillatory component added to this, as illustrated in the following schematic figure

[![precession of perihelion][1]][1]

The oscillation period here is essentially the orbital period of the disturbing planet. The effect is exaggerated here just to demonstrate it. If you do the same calculation with the actual data for all planets, you get the following graph for Mercury's Newtonian perihelion precession

[![Mercury Perihelion precession][2]][2]

Although the increase of the perihelion angle is now closer to a linear increase, there is still a considerable wobble, and at times it is going backwards for a few years. The two main periods in the oscillation visible here are those of Jupiter and Venus, which have the largest impact on the precession (Jupiter due to its mass and Venus due to its proximity)

For more details see the web page [Mercury's Perihelion Advance][3] from which also the above figures were taken


  [1]: https://i.sstatic.net/3TRd4.jpg
  [2]: https://i.sstatic.net/OCbuW.jpg
  [3]: http://www.alternativephysics.org/book/MercuryPerihelion.htm