Its is not a physical shifter, it is electronic just like the push button ones. GM use electric servos or solenoid to engage the front wheels hubs. They get slow to operate. My 93 2500 did this slow to engage. Worked fine. If it goes into 4 low Ok, then the solenoid that locks the hubs is working, the 4 low and Hi is in the transfer case, Not sure how that is actuated. Also were you moving when you shifted it.
1997 Ford F250 Extended Cab, 7.3 Diesel, 8 foot bed.
Reese 16K Hitch
(Moved into Shed) Hensley Arrow
Jordan Brake Controller, Hensley TruControl Gold Shelved.
Open Range 5th Wheel, Roamer RF392 BHS
Happy Camping !!