Might I ask what your mousepad software happens to be.
On mine, which uses Synaptics, there is an option in the Device Settings tab of Mouse Properties, under Tapping, where you can check a checkbox that will make a double tap at the upper left corner of the mousepad enable/disable it. The section is called TouchPad Disable Zone Settings and the actual checkbox is Double Tap to Enable or Disable TouchPad.
What I'd recommend if you can't do it via a keyboard shortcut or specific corner double tap is to cut yourself a piece of thick-ish paper (file folder or the back of a note pad tends to work well) of the correct size to cover the mousepad area and tape it such that you can flip it open when you need the mousepad and flip it over the mousepad to cover it when you only want access to the left or right click buttons. I've used that method for years on devices that give no other option, and it works beautifully.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
To think is to differ.