Your transfer case does not have any moving parts in it while sitting idleing, only while under power on the road.
Your trans will move only when driving also.

 

Manual trans only moves when clutch is released and autos will only move when gas is given to make the torque converter send fluid threw out the trans.

 

My 97 ZJ clicks in every gear but park, changes speed with acceleration, and gets quieter only when I push harder toward 4hi on my quadratrac. Have attempted adjusting the linkage, but with limited success. Thoughts?

 

If you have noise with the Jeep idling in park or neutral, you have an issue with the engine or items attached to the engine, which includes the transmission / torque converter. If the noise is the same as when you had the txfr case replaced before, the fix may have been serendipitous. It definitely does not sound like the txfr case is the source of the current noise & if it sounds the same as before, it probably wasn’t the t-case the first time.