That's a carb overflow hose/balance tube combo. (1)Float sticks open it dumps fuel to the ground, not into the engine. (2)So there is no vacuum when the fuel empties inside the carb, it's vented to atmosphere. Find the nipple usually found on the bottom of the carb. Run the black hose behind the farthest steel lined hose; away from the exhaust pipe; and let the end hang between the trans and engine. Zip-tie the hose to that steel line.
Let's walk the steps prepping a new BS type battery into service.
1. You buy a new battery it comes with acid. BS stands for Battery 'acid' Supplied.
2. You let the acid soak the pleats in the battery for at least an hour before any other move. More is better.
3. You find a battery charger that matches the amp hour. Formula goes: 12N12a reads; 12v, N for battery post positions, 12a is to move the decimal point over one, and you now know what minimum charger you need.
4. You have a 12N14a battery, then you take your 1.4a rated charger, and charge the battery for literally 14 hours; is the formula.
5. You grab car jumper cables, a high beam head light side of the filament, the brake light filament of a taillight, so as to drain the battery down to 1 or 2v.
6. You charge this back up to its rated hours and do this battery drainage 2 more times. Charge the battery up the 3rd time and now it's ready for years of service... not that 2 year shit, pour and service. You poured and you serviced under an hour?... oh shit say you didn't. Oh well, live and learn.
7. Yes you can use a 1.4a charger on a 12a battery, but you can't use a 1.2a charger on a 14a battery. You just cut the time down on the hour rating, but you never will get the 14a battery fully charged with a lower rated charger.
8. Yes you can use a 10a car charger, but the trick is to keep a feel on the battery case. It cooks the acid with water and like water and oil you want it blended together as much as possible. Thus the recharging hours of mixing. Like champagne bubbles off a glass is the size you want bubbling out of the pleats. Cook it too long and the bubbles enlarge, rip up the pleats, separate the plates... is why the rated charger keeping the bubbles small for hours on end.
Remember is not the answer. Where is your digital test meter? The battery went down or not? Process of elimination. Battery/button/relay/motor. Not the button, nor the relay, because you can make the relay click with the button. Battery or starter motor is left. Moves meter piece next to if I remember piece... Checkmate.