I think you may have a worn shift linkage and you may be able to adjust it. You are basically pulling the linkage past where it needs to be to get reverse then pushing back to reverse it works. On the side of the trans is a bar from the trans to frame. It has another bar from the shifter to it. there is an adjustment there,. You need to follow the instructions and try adjusting the linkage. If this does not work, your linkage along the side of the trans is worn and needs replace

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1. Loosen swivel clamp screw.
2. Position shift lever in neutral gate.
3. Position transmission lever in neutral detent.
4. While holding swivel clamp flush against equalizer lever, tighten swivel clamp screw, Fig. 6. Do not exert force in either direction on rod or equalizer lever while tightening swivel clamp screw.

No, similar as to rear wheel drive but your shifter uses a cable from shifter to trans. The cables become stretched over time and need replace but you can try the adjustment,There is not a sensor that affects the shifting the way you describe. It is clearly a cable that needs adjust or replace. Again, hard to explain but you are pulling on a say stretched cable beyond where it needs for reverse in order for it to slip back to reverse.

Notes

View Full Image REMOVE OR DISCONNECT Disable SIR system. Left sound insulator and knee bolster as necessary. Cable retaking clips and cable at steering column. Cable assembly through hole in cowl. Cable from transaxle manual shaft lever and bracket. INSTALL OR CONNECT Properly route and position cable. Cable at transaxle manual shaft lever and bracket on transaxle. Cable at steering column and retaining clips. Enable SIR system. Adjust cable.

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1. Set parking brake and chock wheels.
2. Remove shift cable terminal from transaxle manual shaft lever pin.

• • Pry on the shift cable terminal at the manual shaft lever pin with a appropriate tool. Do Not pry or pull up on any other part of the shift cable - the shift cable could be damaged.

1. Fully lift adjuster lock button. Assure the adjuster is free to move.
2. Place transaxle manual shaft lever in "NEUTRAL" gear. To find "NEUTRAL," rotate lever fully counter-clockwise to "PARK", and then clockwise 2 clicks into "NEUTRAL".
3. Place the gear shifter (inside car) in the "NEUTRAL" position.

• • Floor Shift - Use transaxle shift indicator on console to find "NEUTRAL".
  • Column Shift - Rotate shift lever to "LOW 1" position (Fully down). Push forward on lever and at the same time, push up slowly. The gear shift lever will move up while clicking over the gear over travel stops. When the lever stops solidly, it is in "NEUTRAL". Release the lever.

1. Underhood, grasp the shift cable terminal and pull it toward the pin on the manual shaft lever (the shift cable adjuster spring should compress as the terminal is moved toward the pin). Attach the pin to the lever by pushing down carefully until it snaps-do not move the lever out of position. Do Not pull terminal beyond pin then push back-this could move the shifter out of "NEUTRAL".
2. Press the adjuster lock button down flush with the adjuster body.
3. Shift to "PARK" and release parking brake while applying service brake. Start engine and assure all indicated gear positions match vehicle response.