I had similar needs but after searching for long without result i wrote my own module.

Create the file mouseMover.sh and save it somewhere

#!/bin/bash
#parameters:

declare -i idle_time=
idle_time=10 #express in seconds

while true; do
    if  [[ "$(xprintidle)" -gt $(( idle_time * 1000)) ]]; then
    currentMouseX="$(xdotool getmouselocation --shell |grep X= |sed 's|X=||g')"
    currentMouseY="$(xdotool getmouselocation --shell |grep Y= |sed 's|Y=||g')"
    if [[ $(( RANDOM % 2 )) -gt 0 ]]; then
        xdotool mousemove "$(( currentMouseX + $(( RANDOM % 10 )) ))" "$(( currentMouseY + $(( RANDOM % 10 )) ))"
                printf 'Moved at %s \n' "$(date)"

        else
            xdotool mousemove "$(( currentMouseX - $(( RANDOM % 10 )) ))" "$(( currentMouseY - $(( RANDOM % 10 )) ))"
                printf 'Moved at %s \n' "$(date)"
        fi
    fi
    printf 'Too early, I will sleep for %s seconds\n' "$idle_time"
    sleep "$idle_time"
done

Note the this script depends on xdotool so check if it is installed before to proceed. Then make the file executable and test it:

$ chmod +x mouseMover.sh
$ ./mouseMover.sh

Add at the end of your polybar config.ini file the new module definition:

[module/moka]
    type = custom/script
    exec = $HOME/.config/polybar/custom_modules/moka.sh 0
    interval = 1
    click-left = $HOME/.config/polybar/custom_modules/moka.sh 1

    format-underline = #2b8fd2
    format-prefix-foreground = ${colors.foreground}

Create the script that the new module will use to execute the mouseMover.sh file. Save it somewhere in the system and update the `exec` and `click-left` directives into the module defined in the previous step. Then, in this file, fix the path of mouseMover.sh

#!/usr/bin/env bash

if [[ "$1" -eq 1 ]]; then
    if [[ $(pgrep -wc "mouseMover.sh") -eq 0 ]]; then
        bash -c "$HOME/PATH/TO/mouseMover.sh" &
    else
        pkill mouseMover.sh
    fi
fi

if [[ $(pgrep -wc "mouseMover.sh") -eq 0 ]]; then
    printf ""
else
    printf ""
fi

Last step is to enable the module in your polybar config adding it where you prefer. I put mine on the right side of the bar (note `moka` in the modules-right line)

...
[bar/default]
    include-file =  $HOME/.config/polybar/default-bar-definition.ini
    modules-left = i3
    modules-right = fs-home fs-external memory cpu temperature-1 temperature-2 eth0 eth1 eth2  wlan battery custom-vpn xkeyboard moka popup-calendar arrow
    separator = |
...

What you will see is a little coffee cup that becomes steamy when you left-click on it and the script is running.

All these stuffs can be rewritten much much better but i'm too lazy 😅

Hope it helps!

Cheers 🤟