Hi Austin
My understanding is that there is no clock in the MCP itself.
As this was a two way communication product, when you press the clock button on the MCP it "asks" the BeoMaster the time then displays the response.
That is why when you wind or rewind the cassette tape, the display on the MCP struggles to keep up with what is actually happening on the BeoCord.
I would expect that taping down the button would drain your batteries.
Opman