Why does it periodically refuse to shift out of park?

If after every re-adjustment the trunk close only to refuse to close after sometime, it is posible that striker is not tight enough and probably shifting after some uses. It is likely also that the threads on the bolts or screws are worn lightly. If posible try using a spring washer or some threadlocker medium strenght.

I have a gmc jimmy 1997. The battery is dead. It refuses to shift to neutral for towing. I would like to know what I can do to remove the vehicle from the parking garage for towing.
thanks

Transmissions have so many parts so it's difficult to diagnose. I would have the transmission filter changed first. Usually that is the most common shifting problem. If that doesn't fix the problem it may be a little more costly.

You have a transmission failure that will likely require an overhaul.

if check engine light is on then it has codes in it, period. need to get scanned somewhere else

your problem lies in the internal parts of your transmission which are the clutch linings, they are already worn out and starts to slide.

Shifting to NEUTRAL
To shift the transfer case to NEUTRAL, first make sure
the vehicle is parked so that it will not roll:
1. Set the parking brake.
2. Start the vehicle.
3. Connect the vehicle to the towing vehicle.
4. Put the transmission in NEUTRAL (N) or have
the clutch pedal pressed for vehicles with
manual transmission.
5. Shift the transfer case to 2HI.
6. Simultaneously press and hold the 2HI and
4LO buttons for 10 seconds. The red NEUTRAL
light will come on when the transfer case shift to
NEUTRAL is complete.
7. Shift the transmission to REVERSE (R) for one
second, then shift the transmission to DRIVE (D)
for one second or FIRST (1) for vehicles with
manual transmission.
8. Turn the ignition to OFF.
9. Place the transmission shift lever in PARK (P) or
FIRST (1) for vehicles with manual transmission.
10. Release the parking brake prior to towing.

************************

Shifting Out of NEUTRAL
To shift out of NEUTRAL:
1. Set the parking brake and apply the regular
brake pedal.
2. Start the vehicle with the transmission in PARK (P)
or FIRST (1) for vehicles with manual transmission.
3. Press the button for the desired transfer case position
(2HI, 4HI, AUTO 4WD or 4LO).
4. Put the transmission in NEUTRAL (N) or press the
clutch pedal for vehicles with manual transmission.
5. Shift the transmission lever to the desired position.
After the transfer case has shifted out of NEUTRAL,
the red light will go out.
6. A re-engagement sound is normal when shifting out
of NEUTRAL.

if the shifter refuses to come out of park have someone push the car forward slightly to release the tension on the parkin paul which holds the vehicle still and i dont understand your second part

You need to check the linkage. Under the car, the section that connects the gear shift stick to the transmission rods.