Hybrid \$\pi\$ Model vs. T-Model Input Resistance (MOSFET)
To find the input resistance, the procedure is to apply a test voltage \$v_t\$ to the input terminal (the gate). With the source node as our reference voltage \$v_t\$ is simply \$v_{gs}\$ (voltage from gate to source). The input resistance \$R_i\$ is then the ratio of the test voltage divided by the current \$i_t\$ supplied by the test voltage:

$$R_i = \frac{v_t}{i_t}$$

In this case \$i_t\$ is the current flowing from the gate node to the T junction (between the dependent current source and \$r_s\$).

The dependent current source \$i_s\$ in the MOSFET T-model is equal to \$g_m v_{gs}\$ (just like the hybrid-\$\pi\$ model). By Ohm's Law the current from gate to source (through \$r_s\$) is

$$i_{gs} = \frac{v_{gs}}{r_{s}} = \frac{v_{gs}}{1/g_m} = g_m v_{gs}$$

Since \$i_s = i_{gs}\$ it must be true by KCL that \$i_t = 0\$ no matter what the input voltage \$v_t\$ is. Therefore

$$R_i = \frac{v_t}{i_t} = \frac{v_t}{0} = \infty$$

The input resistance for the T-model is infinite, just as it is for the hybrid-\$\pi\$ model. It is not equal to \$1/g_m\$.