The light should blink only while the TCCM is attempting to shift to the requested mode. After a successful shift the TCCM will keep the current mode indicator light on solid.
How is successful shift determined? Inside the shift motor, attached to the output shaft is a range position sensor. That sensor is also known as an encoder hence the oft heard name "encoder motor". This sensor is the sole means of the TCCM to determine where the shift motor is currently.
"A rotary encoder, also called a shaft encoder, is an electro-mechanical device that converts the angular position or motion of a shaft or axle to analog or digital output signals. There are two main types of rotary encoder: absolute and incremental. Wikipedia"
Looks like this...
There are 3 wires connected to the sensor, a low reference, a 5 volt source and a sensor return signal. Inside the sensor the 5 volt source is connected to a broken circle of resistive material where the other end of the resistive material is connected to the low reference. The remaining wire, the return signal is connected through to this resistive material by a set of wipers that rotate with the motor in such a way that the return voltage sensed varies with the position of the shift motor.
This is how the TCCM determines when a successful shift has occured. For a given mode position there is a small range of return signal voltage and the TCCM will rotate the shift motor until the sensed voltage falls within the acceptable range for the desired mode. Here I measure the return signal voltage with a 5 volt source, a range position sensor and a DMM...
My original sensor had a microscopic cracked solder joint in the sensor return terminal which resulted in intermittent operation.
In 4WD, even with the light blinking, it took of better, nothing funny with the back end or traction control light. Can I be in 4WD but still have a blinking light? Something not quite making contact
With the light blinking at the 4Hi position the TCCM will be trying to turn the shift motor to that position. While rotating towards the 4Hi position one of the operational cams inside the transfer case will be applying forward propshaft clutch pressure. So even if you have not fully engaged 4Hi while that light is blinking you may very well be almost fully applied.