That sounds like the transmission range sensor is not moving fully to the park position. The rocking moves it enough that it switches. The question is then, is it the switch or the cable that moves the shift lever. From the description it could be either.
The switch is under the transmission on the drivers side while the cable is on the top.
Two first pictures.
The shift cable is adjustable and that adjustment could cure your problem as it sounds like the cable could be slightly stretched. The process is below, it is done in the vehicle right under the steering wheel.
Remove the steering column upper and lower covers.
Shift the transmission into the [N] position.
-Third picture -
Remove the cable end nut (A), then separate the shift cable (B) from the shift lever.
Rotate the socket holder (C) on the shift cable a quarter turn; the tab (D) on the socket holder will be in the opening (E) of the shift cable bracket (F). Then slide the holder to remove the shift cable from the shift cable bracket. Do not remove the shift cable by twisting the shift cable guide (G) and damper (H).
Push the shift cable (A) until it stops, then release it. Pull the shift cable back two steps so that the shift lever position is in [N]. Do not adjust the shift cable by holding the shift cable guide (B).
Turn the ignition switch ON (II), and verify that the [N] position indicator comes on.
Turn the ignition switch OFF.
Insert a 6.0 mm (0.24 inch) pin (A) into the positioning hole (B) on the detent plate through the positioning hole (C) on the control bracket. The shift lever is secured in the [N] position.
Align the socket holder (A) on the shift cable (B) with the slot in the shift cable bracket (C), then slide the holder into the bracket. Install the shift cable end (D) over the mounting stud (E) by aligning its square hole (F) with the square fitting (G) at the bottom of the stud. Rotate the holder a quarter turn to secure the shift cable. Do not install the shift cable by twisting the shift cable guide (H) and damper (I).
Verify that the shift cable end (A) is properly installed on the mounting stud (B).
If improperly installed, remove the shift cable from the shift cable bracket, and reinstall the shift cable. Do not install the shift cable end on the mounting stud while the shift cable is on the shift cable bracket.
Install and tighten the nut.
Remove the 6.0 mm (0.24 inch) pin that was installed to hold the shift lever.
Move the shift lever to each position, and verify that the A/T gear position indicator follows the transmission range switch.
Push the shift lock release, and verify that the shift lever releases.
Images (Click to enlarge)
Saturday, April 14th, 2018 AT 7:50 PM