Installation is easy for John Deere AM101406 Voltage Regulator. The Ducati connector doesn't fit John Deere. You need to remove the spade lugs from the plastic connector housing and clip each lug individually onto the JD terminals.
The JD regulator has one less terminal on it than the Ducati regulator. There's no "R" terminal on the John Deere. That means one of the heavy white wires is not used and can be tied off to the wiring bundle. They come from the same source anyway so it doesn't hurt anything. Be sure to cover the end with some shrink tubing to insulate it from shorting out against the firewall. The remaining heavy white wire is connected to the "B" terminal. Also, on both regulators, terminal "L" is not used. I think it is used to drive an indicator light circuit. The two heavy yellow terminals come from the generator and are connected to the two "G" terminals. Doesn't matter which wire to which terminal. The remaining small yellow wire connects to the "C" or sometimes labeled "F" post. This is the bus voltage detect wire from the ignition switch.
I mounted the JD VR in the same location on the firewall shelf using an aluminum sub-plate for better heat dissipation. I used thermal paste on the base of VR so heat transfers to the sub-plate.
As standard operating procedure now, when through flying I open the oil door on the top of the cowling to let heat escape.
You ask if this will solve your problem… if battery is original from 2012 and 360 TT you may be looking at a new battery. Also, if you fly short flights its possible battery is not being replenished. I use Odyssey 6 Amp Portable Charger [OBC-6A] which has features for desulfate and trickle charging.