Trouble deriving/understanding time constant
First of all, when the Zener diode would not be there or would not be functional, R1 and R2 are in series, not parallel.

The ideal Zener behaves like a voltage source, which can pass through any current.
The Zener diode clamps the voltage across it to 5V. It doesn't matter what the value of R1 is, the current through R1 will be \$V_Z / R1 \$, and the remaining current caused by \$I_L\$ flows through the Zener.
Therefore, R1 does not affect the discharge current and is the time constant only determined by R2 (and L1) as long as the Zener diode is clamping.

Below a simulation in LTspice to show what happens.



As the simulation shows, node clamp is clamped to 5V and I(R1) = 1 mA, until about t=0.1us where the Zener stops clamping. Then, R1 also starts playing a role in the discharge time.

Obviously, the voltage across
 L1 eventually become 0V. Therefore, at some time, the voltage across the Zener will be less than 5V at some time, and so, there always will be a tail where the (remaining) discharge time is determined by \$L/(R_1+R_2)\$.