transfer case

What timing are you asking about? Normally you just make sure you have 2WD selected on the dash and that the case is in 2WD when you install the encoder. Then install the case and it should select each gear okay. If yours is not then explain what it is doing. You could have a bad encoder or transfer case control module.

After driving it about a mile it goes in neutral but the gear shift shows drive, have to put it in 4h to get it back home, someone said it was the transfer case replaced it and the encoder motor and shift fork! Wanting to know if it needs to be put in neutral on case and dash to put it back in ? And gear shift?

So you can start out in 2H, drive for a bit and the transfer case will shift itself into neutral? Then if you shift it into 4H you can keep driving? Does it return to 2H when you start it again or do you have to select it?
That sounds like the transfer case control module(TCCM) or selector has a problem. Easy way to test if it is in the T-case or not. Select 2H. Be sure it is engaged. Then unplug the transfer case encoder. Try driving it a bit. If it now stays in 2H without going into neutral it isn't inside the case. The next steps require a dealer level scan tool to test the selector, TCCM and the encoder motor. It would show you which mode the switch says it is in, and what signal the TCCM is getting. Plus what the TCCM is telling the encoder motor. From your description it sounds like the TCCM is faulty, either it has a component that is heating up and switching the T-case or it is shorting.

Do not have 2 hi hummers are AWD so have 4 hi, 4 hi lock, 4 lo lock.

Yeah remembered that afterwords but came back to edit and was over the time limit. Just got mixed up from answering about another T-Case issue.
Either way the box should stay locked in whichever gear you select before you pull the plug. When you select the other positions does it actually shift into them and stay there?
There is still no timing in the box itself. I would be sure it is in AWD and pull the plug. That will show you if it has an internal problem.

Will try that and let you know. Thanks

Sorry for the mix up. Need to put up a scorecard to keep the answers straight.

Does the encoder motor and dash buttons have to be in neutral when replacing the encoder motor?

As long as they match in position you can use any gear. I generally start with them in whichever the "normal" position is unless there is a specific instruction. For yours it just says to rotate the shift shaft to match the encoder position at install.

Will axle coming out of spider gear in front differential cause it go into neutral?

It will cause it to stop moving, not really neutral though. On an AWD vehicle with open differentials in the axles and T-Case all four wheels in contact with the ground allow power to go to all the tires.If one tire breaks free you lose drive on the other three. That is why the lock positions are there. On modern AWD with traction control that vehicle design would apply the brake on the spinning tire to force the others to move.