I have a 16.5 LT Briggs&Stratton ride-on mower. I started it last week after it sat for about 2 months through winter. It was stored in a shed. The battery was a little week so, I drove around in it for about 15 minutes to re-charge the battery. I then proceeded to give it a tuneup. I changed the oil with SAE 30 recommended oil, I drained the gas entirely from the tank and added fresh gas, changed the fuel filter, changed the spark plug and cleaned the air filter. Also I cleaned the engine compartment with 409 cleaner to remove the dirt and debris.

I proceeded to now start the mower and it wouldn't start. I disconnected the fuel line at the carb to check for gas and had plenty pouring out. Then I checked the spark plug, and had spark. So then I thought maybe not enough fuel in the carb, so I sprayed some quick start into the carb, went to start it and it cranked over and started right away, BUT it only ran for about 5 seconds and stopped, so I sprayed again, it started but only ran for 5 seconds again and stopped. I took the a look at the plug and it didn't appear to have any gas on it.

Does anyone have any advice what else the problem might be. Again it ran fine earlier. I noticed that there is an electrical connection plugged into the bottom of the bowl on the carb. I checked other wire connections and they seem to be all connected. What does this connection do at the bottom of the carb? Is there some sort of electrical signal that shuts the fuel flow into the carb? Looking for some advice.
Thanks

Some small engines have a shut off when the oil level gets to low I don't know much about it but I think that it kills the spark any way. Probably not much help but something that you can check without any major work

That electrical connection is the fuel cut solenoid. It's your best suspect. Tap the area lightly and you might get lucky.

If you can rig a funnel and a small amount of carb cleaner as fuel, you might be able to clean it while attempting to start it.

For future reference use only spray carb cleaner and not starting fluid for small engines.