The owner's manual for your bike can be
found here on Beta USA's support page. The wiring diagram and legend are on pages 24 & 25.
The stock engine stop switch is the red button on the forward-facing side of the switch assembly on the left handlebar. It's a momentary push switch, so I don't see how it could be re-purposed as an ignition map switch.
The horn switch is the black momentary push switch on the rear-facing side of the same switch assembly on the left handlebar. The horn comes from the factory mounted on a bracket affixed to the lower triple clamp, between the black fender brace and the triple clamp. The bracket is famous for being the first thing to break off of most Beta's under normal riding conditions. Most riders who don't plate their bikes just toss it in the trash when it breaks.
The tail and brake lights are in the same LED assembly. If the tail light doesn't come on when the bike is running it's likely due to broken wire or poor electrical connection in the plastic electrical connector. I had a problem with flickering taillight when my 2016 was brand new and my dealer resolved it under warranty by putting a dab of dialectric grease in the connector and zip-tying the connector ends together. (No problems in 200+ hours of operation since.)
The brake light switches are built into the banjo bolts on the front and rear brake master cylinders. I'm not aware of any method to adjust them, but they can be replaced for around $15 each.
Here's an example replacement at RMATV.
The bike doesn't come from the factory with an hour meter, as this function is built into the stock speedo. But the speedo is prone to breakage and button battery failure, so many riders like me opt for aftermarket hour meters to keep accurate track of run time. Not sure about yours, but mine is powered by a 10-year internal battery. The only wire from it wraps several times around the sparkplug wire, using non-contact inductance to detect the engine running.