Safe base resistor for TIP120
This will not work, for the following reasons:


I suppose your GSM module is connected to a microcontroller, which is not powered off. If you switch your module's GROUND and leave the rest of the IOs connected, then it will be powered through its IOs, and either not work, or die.
Your transistor is a darlington with high Vce-sat, something like 2V or more. Therefore there will only be 1.3V left on the 3V3 supply and the module won't work.


You need to use a suitable high-side switch. Either an integrated one, or a suitable PMOS.


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