If you blew the right switch fuse, I'd start looking for a wiring / short / corrosion problem in that circuit. That circuit includes the side stand relay, right switch itself and a few connectors. Ultimately, the circuit provides power to the ECU and fuel pump relay you replaced if all is well. There is also a inline 20A fuse for the fuel pump relay that can be a problem, but that wouldn't cause the 3A fuse to blow. Maybe the main fuse at the top of the fuse block, but not the right switch fuse.
Blowing a fuse indicates a large current draw beyond what the circuit is rated for. If the 5A fuse you used didn't blow, you likely don't have dead short somewhere, but there is still something pulling a heavier load.
I'd start by unplugging related connectors and checking for water or anything out of place. You have to look at the pins, of course, but also get inside the back shell looking for anything. Also look along the harness for places it may be chaffed or pinched and making contact with the chassis.
If you have the owner's manual, there is a fold out schematic at the back of it. Otherwise, look online. They used to be i the ST forum, but the Dropbox location they were being hosted is currently down.
Edit: Here's a link to a thread with the schematic hosted as a picture in post #7.
http://www.ducati.ms/forums/56-superbikes/68237-2001-996-neutral-switch.html
