Mahmut S....the 1/gm "resistance" is - in fact - not a real resistor. In no case it is a quantity which exist in a real fet and could be found between G and S. It's a pure mathematical trick to make the model to obey the same equations as the other models.

In small signal AC analyses T-model works as well as the other shown models, but having a resistor between G and S is confusing and makes difficult to see the basic idea of gm - the control function between Vgs and Id. As a teacher of engineering students I do not like it, no matter it's mathematically right.

My recommendation: Don't use the T-model. Use the equivalent models with gm as a voltage-controlled current source.