Are you sure you are hearing the relay activate?
Get a volt meter and measure if you have 12v to the VSV's. One should get 12v in 2wd and the other in 4wd. If you have 12v to each one when the shift lever is in the appropriate position pull the vacuum line and see if you actually have vacuum. If one does not get 12v then you have a 4wd switch bad, relay bad, or wiring issue. If each has 12v in the appropriate position and you don't have vacuum, then bad VSV. If you do have vacuum then you have a vacuum leak or the actuator is working and the indicator switch in the diff is bad.
If your 2wd VSV is working and your 4wd VSV is not you can put the truck in 4wd, switch the vacuum lines between the 2 VSV, 4wd should then activate and the indicator on the dash will light. This will at least verify that 4wd is mechanically sound.