Joe -- inside the tach there is a printed circuit made of copper printed on mylar that fits into a slot. It's that printed mylar to slot connection that connects the LCD to the main board inside. You need to open the tach to access it.
The fix above didn't work for me. I ended up buying a mechanical hour meter that's way more reliable, and adding it. I let it run in my basement (hooked up to a 12v battery) for weeks to bring the replacement up to the number of hours required, then installed it on the pedestal. I still have the old tach and the engine speed works but the LCD doesn't work.