Hi timburn, great looking LS !!!!!!!
The GEN light coming on at idle is normal, this charging system doesn't start to do much charging below 3500 rpm .
If you are in city traffic with a lot of your riding, I'd get a battery tender type charger, otherwise you're going to have low battery charge problems .
I had this problem when i lived in Chicago, if I didn't put the battery on charge, or get it out for a couple of hours at highway speeds on my weekend !!!!!, about 5-7 days of city commuting would run the battery down to the point that the starter wouldn't work .