Goes in and out of 4wd erratically and for no apparent reason

fix the reason that the rear is cycling up and down

no year
no car started
no engine

no model
and no actual transmssion stated(options)
nor if 4wd, or not.
A generic useless answer......
some years this can happen easy
on modern cars the TCM can down shift for many reasons
besides, excess engine load.(like hills)
in 4wd
or other reasons
did you scan the PCM/tcm yet.
that would be first.
TCM detected wide open throttle ,even if false, (tps errors)
TCM sees transmission errors and goes to limp home mode.
scan it
scan it.

Did you have same size tires put on ? With the light flashing there is a DTC'S - diagnostic trouble code stored , have to have diagnostic tool hooked up . That's the only way your going find out what the problem is .

check the vacuum lines going to the tranny, but it sounds like a vacuum leak, when the engine is at idle, spray a few short blasts of starting fluid around all the vacuum lines, if the rpms jump up, thats where the leak is

replace idle air control motor

the Instrument panel cluster on the silverados and sierra and tahoes all have this problem the cluster assemblys go bad for no apparant reason and you will need a new cluster they are 260 and they are non reparable , and a gm dealer will need to program your mileage and engine hours into the new controler (cluster)

that happened 2 me , had 2 have it towed to dealer. I had them disable entire security system.

Have the tranny flushed and new fluid put in, and a new filter.

Things are getting gunked up and sticky in there, the car is 18 years old now.

take apart and clean mud/rust out of wheel hubs.

throttle position sensor. or idle control sensor