So I took a look at the BH76362FV, which is a video signal switching MUX. It has 6 input video channels, one output video channel, and 4 digital control lines. It is a 4-bit mux, and depending on the values of the CTLA, CTLB, CTLC, and CTLD, the MUX will send one of the 6 input channels, Mute, or Standby to the output.
I don’t know how a waveform generator could be used to control this video mux. A BCD counter could not control this because it does not count high enough, as it wraps around to zero from nine, but most of the required values are above 7 (value of MSB, CTLD, must be high except for Standby mode). A binary counter could be used, but half of the values (0 - 7) will give the same output - Standby - and I presume you’ll need something to read the value back so you know which input is selected.
I don’t know what you mean by switching time. What is your input device?
It would seem like a microcontroller would be the simplest device to control the MUX. It could read whatever input you fed it (rotary encoder, multi-position mechanical switches, serial data, etc.), set the control pins accordingly, and provide some sort of feedback to the user to indicate which input or mode is selected.