Bob, people with unhappy experiences tend to be more vocal. I had a car that was a pure lemon many years ago. It was in the shop for the I don't know how many times (but they found something different each time) when they called to tell me it would take 2 weeks for the latest repair - no offer of a loaner either. I made the mistake of saying, good now I get a new car since the 30 days out of service runs out tomorrow.
Dealership went out and took the part off a new car in the lot and had it ready to be picked up by 9 the next morning. You don't know how many times I've cursed myself for that comment. 1.2 years later the engine blew completely. Yet Road and Track had nothing but praise for the car and the first 6 months it was great then there was a "pop" one day out of the freeway in Riverside, CA. After that it was one thing after another - you know how many things have to go wrong to get 30 days out of service in less than 6 months?
I know a couple dozen people with BV 500s and yours is the only one with the tail light issue. I did have a speedo issue with one of my NOS BV 500s but it was replaced under warranty and not had a bit of trouble with it since - 3 years ago. That scoot has made many a long distance tour too - Houston to Breckenridge, CO, Breckenridge to San Diego through the Utah national parks (and more time on dirt that I really like), back up through Monterey (Big Sur, lovely can't recommend it enough), through Yosemite, across US 50/6 in Nevada (cruised 85-95 for hours only stopping to top off the tank from the spare gas I carried) back to Breckenridge. From Breckenridge to Lake Geneva, WI for Amerivespa, again through national parks like Mt. Rushmore, Badlands, Crazy Horse (okay not a national park but very interesting), around the southern bits of Lake Michigan part way up the state then across on the Lake Express Ferry back to WI with a more northerly route back to Breckenridge via Fargo, Teddy Roosevelt National Park, Yellowstone, Grand Tetons, Rocky Mountain national parks. It is ready for a belt, rollers and spark plug change but not a single mechanical or other issue (knock wood) on any of them unless you count the sucky gas mileage crossing Nevada at 85+ mph (dropped it down almost to what the Burgman 400 got - oh and I find the BV 500 more comfortable than the Burgman we had though I adored the amount of storage in the Burgman.)
At Amerivespa there were several BV 500 owners who had ridden in. None of which have mentioned any of the issues you'd had nor did the few BV 250 owners. Sadly there was no one with the BV 350 at Amerivespa last year but the few people I know who own them (2 in Houston, more on the Modern Vespa forum) only one has reported any significant problems and that was a Brit on the Modern Vespa forum.
I know many here adore the Burgman but it doesn't fit me and I had several minor things go wrong with it in the 2 years we owned it more than I've had in the over 5 years I've owned the GTS.