Little help here?

So next I removed the switch and ran a wire through the two eyelets on the piles of the switch. Twisted the wires to get a good connection. Push start button and choke a little. Starts right up! Go to NAPA and get new switch. Install switch and it starts right up. Drive tractor around for a while to attempt to charge battery even more because I had wore it down cranking it so much. Then turn tractor off. Turn key back on, push button and it starts right up. Drive tractor around for a while longer with big smile on my face. LOFL. When we get those new smileys. Will we be getting one that is a pat yourself on the back smiley?!

She is starting and running great now!

 

One of those wires probably the one that went "nowhere/somewhere" was grounding out while the ignition was on and drawing down the battery.
The ignition switch should have(typically) one hot in from the battery one to the ignition coil(closed when "on") and then jumpered to what I think is you're your push button start - from the pushbutton to the starter solenoid to complete the starter circuit.

Starter circuits typically don't affect the alternator/charging - but grounded wires will draw it down when the circuit is completed(key on).
I chased an issue like this on my truck - would start every time at the house, but if a I drove it somewhere it wouldn't restart -finally found the main starter cable scuffing on the frame, arcing out as it bounced down the road killing my battery at my destination

 

The battery charger I ordered to replace the one I returned will be nice. It is in the garage now. It has the ability to charge, jump, and test. With the Bobcat B300 TLB, the Ford Powermaster tractor, the Simplicity riding mower, the Troy built zero turn mower for the camp, and the truck and wife's SUV, it will be handy to have around!