On mine it "just worked". I'll need to check it out later today as I must start my "honey-do" list before my wife breaks my fingers. But there is an option page. Hopefully, someone will catch this and respond before my wife allows me to check it out myself?
I just downloaded 1.4.2 (next version after your reported version) for MC 1.12.2. For me, it "just works". If I click on the LiteLoader tab and go into the settings for the mod, I have checkboxes for "Draw Villages", "Draw Golem Spawn Area", and "Draw Dots". I have all mine checked, sphere density is max and dot size is large. In the "Options | Controls" menu, I do not see any key controls available for Kabo's Village Marker, so no keys to "toggle" the settings for the mod. You should double-check inside the LiteLoader settings menu for that mod.
Try checking out the latest version 1.4.2 for use with Minecraft 1.12.2. Oh, I had one thought to check... SHADERS! I turned on shaders and where it was working before, I get *nothing*. If you are using Optifine or the Shaders mod, be sure to turn OFF shaders in the Optifine config or remove the Shader's mod from your load. If the Village Marker mod STILL doesn't work, try turning OFF all other mods until it does, then turn the mods back on until you find the one that is causing the problem.
At the moment, I expect you are using Optifine with shaders. Let me know how this comes together for you, I hope this great mod will work for you. Just turn shaders back on within Optifine when you are not needing this mod at that moment.
EDIT: Oh! I just saw your edit. Great! I'm glad to see it is working for you now. If you need this for SMP, it does get a bit more tricky but it will work with SMP if they are using the Spigot plugin for it.