I think I got it. The two phone jack inputs are out of the circuit, with wires "far" from the circuit board. When I plug only one guitar, the other one creates an open circuit. Since there is a wire going to the input, this one is un-grounded and must act like an antenna like you said. If I ground that wire, the buzzing sound is gone. If I plug a shielded jack in the second input, the buzzing sound is much lower. When my brother comes with his guitar next time, I'll try it with both guitars in, see if that was the problem. Thanks a lot for the help Audioguru, I'll confirm later if the circuit works fine so that those looking for a simple cheap way to play on a single input amp will have one-a-many solution.I think the input that buzzes has a poor ground connection on its input cable.
If you touch the input with a lead from your voltmeter then it is normal for the circuit to buzz because the lead picks up mains hum like an antenna. Shielded audio cable has the grounded shield to block hum pickup.