When gearing down or coasting the 4x4 shifter will pop or go into neutral

SOURCE: I recently purchase a 1986

You may be listening to a slightly noisy differential or the Tyre's....If they are off roader's they sometimes buzz....To check the diff keep it in gear and give normal gas when descending a hill and then, with the vehicle in gear lift your foot from the gas pedal....If the noise increases to any notable degree, its the diff....You can carry out the same test by disconnecting each of the shafts in turn and repeat the test....When testing the front diff, don't forget to engage the 4X4 drive or you wont go anywhere....You've said the sound is not high in volume, I'd think you can leave it...As an after thought have you checked the oil in the transfer case? Its not the same as the gear box and has a separate filler?.

SOURCE: The car is in neutral

The first thing to check is your brake lights. See if they are working. If they are not working, then your brakelight circuit needs to be repaired so the shift interlock system can work. This could be due to a bad brake lamp switch. If your brake lamps are working, then you probably have a bad shift interlock solenoid in the steering column if you have a column shift or in the shifter housing if you have a floor shift.