No, you cannot use standard two-conductor electrical cable (such as 14/2 or 12/2 containing only a black hot, white neutral, and bare copper ground) to wire a standard 3-way light switch circuit between the two switches. A 3-way switch configuration strictly requires two separate traveler wires plus a common wire running continuously between both switch boxes, necessitating a three-conductor cable like 14/3 or 12/3 (which includes black, red, white, and bare copper wires). You can troubleshoot wiring layouts easily by inspecting cable sheathing in the junction box. You can verify that your corrective action is successful when installing the correct three-conductor cable ensures you have distinct black and red traveler wires alongside a dedicated neutral and ground.
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