Switching input to instrumental amplifier with an analog mux (ECG, EEG)
When reading really week analog signals, you'd very much try to avoid additional things in your signal path before you buffer/amplify that signal.

So, no, I don't think your analog multiplexer will do as is – you should have a high-input-impedance amplifier for every channel, and then you can mux all these amplified channels. Or don't – many microcontrollers come with an ADC that you can switch between different channels out of the box, or you just buy a multi-channel ADC.

At any rate, there's a lot of guides online on how to build your own EEG with e.g. an Arduino, a raspberry pi, other microcontrollers, DAQs…