The way you test the basic functioning of the console gas gauge with its connections is to ground the sender wire so that the gauge jumps to full. I guess that means the sporadic False empty reading is caused by an open connection somewhere. The sender connections should run through the distribution hub along with everything else and should be clearly labeled. On mine the console gauge is inside only - no flybridge gauge. Now some ideas.

If you have the old 4 bolt rochester sender mounted on a pipe, the sender is a magnetic driven dial "button" outside of the tank. Most of these units have a gas gauge on top of the tank as well as a sender. The swing arm inside the tank has no electrical wires. It just moves the magnet and is a very high quality item. The button/senders do go bad. You may need a new button. Contact Rochester for a source for a replacement button.

If you have the newer flush mounted 5 bolt sender the swing arm is a cheap piece of crap but is readily available for under $20. The sender is a rheostat mounted on the swing arm connected inside the tank. What happens is the pickup arm lifts up from the rheostat windings as the pivot wears out causing an open circut. The parts are cheap but require digging the old swing arm out of the tank and fitting the new one. This can be hard on some Marinettes such as my project 32' where port side sender is buried under the cockpit floor. If you have a dial on top of your tank you probably have the 4 bolt Rochester sender.

I once rigged a rheostat to a AA battery to test my Capac meter. You can rig a rheostat from Radio Shack to replace the gas tank sender and test the rest of the wiring. Easier yet, if you have the 5 bolt system you can order a new rheostat/swing arm and wire it up outside of the tank. Move the swing arm manually and the console gauge should register correspondingly.

Thanks guys. I hope its something simple.