Not sure what years will run without a battery (I bought a new batter for my 2015 and it died in less than a month, went to start in the middle of a ride and it wouldn't even light up a bulb).
Anyway...the symptoms you're describing really sound like a poor connection on a hi-current cable. Back to mine, with a battery in it that would not even light up a bulb, I could push start it and it seemed to work fairly normally (with the exception of the signals flashing a bit 'off'. So, by kick starting, you're doing essentially the same thing.
You didn't actually SAY that you could kick it over and it would start with the ignition switch plugged in, but that's what your 2nd paragraph said to me.....
I guess it depends on what works and what doesn't, but it sounds like a poor hi-current connection. They'll be okay for a low amount of current (think of only 1 strand out of 20 in a wire making contact..)..enough current to light the lights will pass through a poor connection, but as soon as it tries to haul the amps needed to crank, it 'overloads' that single wire and burns it and the connection is now open. Same with a battery terminal that's a bit corroded and only making contact in one small spot.
I'd go over the battery connections and follow the cables (ground and hot) and open up, clean, and secure each connection one at a time.
If I didn't get what I thought out of your description, well, clean the connections anyway. :-) It's the Step 1 of electrical troubleshooting that everybody skips because 'they look fine'...somewhere around step 8, you end up back at Step 1 and realize you could have fixed it hours ago.