He angled the light. There it was: her SIM card, wedged snugly into SIM Slot 2, tilted slightly at the corner.
If the tape method fails, the internal contacts may be dirty or oxidized. The Nokia 206 is old, and oxidation is common.
It sounds obvious, but ensure the SIM card itself is not damaged. Test the SIM card in another phone. If it works elsewhere, the problem is definitely your Nokia 206. Also, try a different network provider's SIM in your Nokia 206; sometimes specific carriers' SIMs sit differently in the slot.
For phones that have suffered rough SIM insertion or falls, the pins inside the slot may be bent downwards. This requires careful surgery.