Congrats on the good find! This is MOST LIKELY not an issue at all. As you can adjust the brake levers and pedal on most bikes, you need a way to adjust when the brake light turns on. For instance, if you lower the brake pedal, you need to make the brake light come on later than it normally would since it’s new resting position would have meant the brake was on at the previous position.
The SV650 definitely does not lack brake light under rear braking. Most likely the brake light trigger needs adjustment. Either way, doesn’t sound like a big hangup, but the next time you see the bike, take a look for it. Here’s a relevant page from an SV forum: