I just used a tiny 3-finger piece of parchment paper to selectively insulate every combination of the 3 outer pins, and 3 inner pins separately. I did not try combinations of inner and outer. Each resulted in the Electron blinking blue, except for one case which ended in breathing cyan. I insulated the inner middle pin, which connects power to the VPP of the SIM. This is only necessary for updating the contents of the SIM like changing the PIN. This explains why insulating it had no effect.
It will be more difficult to test the other combinations, but doable. However looking at the connections, I can hardly see why a bad connection on any of the pins will allow it to work at all.
If anyone else has this problem, I'd love to see what your device logs look like before you attempt to fix it with the SIM holder. Please contact me directly so I can give you instructions on how to enable logging on your device.
VCC (power)
VPP (programming power)
GND (ground)
CLK (clock)
I/O (data)
RST (reset)
A first step before bending the pins of the SIM holder might be to slide the SIM in and out a few times to attempt to clear away any debris or oxidation that might be on the SIM contacts.