You do not have a vicious coupler so that cannot be the problem. Clausen is correct that those are the simptoms of a bad VC but the VC only exists in the 249.
The transfer case that you have is the 247... basically the same as a 249 but without the sometimes trouble some Viscous Coupling. Instead the 247 comes with a Progressive Coupling which is supposed to be better due to its ability to have the fluid circulate through it to reduce wear. The 249 is a sealed unit and cannot do this.
I'm with Clausen on his diagnosis except that it is a Progressive Coupling not a Viscous Coupling
No you do not have to replace your entire TC but just plan on spending some money if there really is a problem...