Technically, you are not multiplying. You are multiplexing (switching) between two signals.
Logical multiply would be an XOR (Exclusive-OR) function. Multiplexing (or MUX for short) is basically the schematic below. A low on the control pin (V1 signal) picks input 0 and a high on the control pin picks input 1. The output follows which ever input is selected.
You can use @Michael Karas MUX circuit or you can use an IC specifically designed as a MUX such as 74HC153, 74HC4052 and many more.
Same disclaimer as Michael's circuit. There is no synchronization so you can end up with narrow little pulses when you switch frequencies.
simulate this circuit – Schematic created using CircuitLab