Is the 4x4 actuator supposed to have fluid in it

https://www.manualslib.com/manual/803081/Kawasaki-Mule-4010-Trans-4x4.html?page=37
You did not say what model you have
https://www.kawasakimotorcycle.org/forum/kawasaki-atv-mule/152674-2012-diesel-mule-4010-no-power-steering.html
https://www.kawasakiforums.com/forum/general-tech-9/kawasaki-mule-3010-trans-4x4-640/

check to see if actuator is moving to lock position

Check your fuses.

is this a wet clutch so low or dirty fluid needing changed.

Does it show that it's engaged on the screen? Check your actuator, it's probably damaged. Check your wires and connections as well.

Depending on the flashing frequency, it could be the Electronic BRake controller, the 4x4 actuator or the brain.

Look for the service manual online, it has a procedure for checking/cleaning the actuator. It could be stuck with dirt and need a cleaning.

Some times the four wheeler is not in right position for 4x4 to engage safely so it throws it in to safety mode so it don't slam in to 4x4 with grindage an damage that's my experience. If it seemes to work fine when working run it . . Could need service,fluid change and 4x4 actuators,.,vacuums switches tested also ...

try checking any inhibitor safety switches, one is likely to be faulty, under the seat, or gear selector or oil filter. they do have micro switches that will stop it from working if faulty, its just a guess but a good place to start looking.

not to familiar with the part, but I have good success with using JB weld