Look for tools that support keyboard-driven workflows (vim, tiling window managers, command-line over graphical tools, browser plugins like surfingkeys) and recognize that you're going to have to adapt how you've become used to manipulating a computer and that it's a process.
And take it slow! I think "unplug your mouse" is extremely bad advice, or at least shortsighted. Depriving yourself of a useful tool simply because you want to learn another in more depth breeds resentment and increases the odds of giving up. Use the keyboard because it's faster, use the keyboard because it's better on your wrists, but above all use the keyboard because you want to, not because you're forcing yourself to.
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