Ok. You have two warm temp germinating seeds, but peppers need more heat than tomatoes. Tomatoes readily germinate in 70’s but peppers are better with 80’s.
If the south exposure sunlight is strong, the seed starter trays may get more heat than you might think while the sun is shining. This may also dry them out. Two things to watch out for. I would put a thermometer on the starter trays to monitor the temperature.
You won’t need the supplemental light until they sprout. But they need it when the sun is not on them. How much can you baby them? Are you away all day? Reason I ask is that the lights would block the sun unless you can move the trays to the lights as needed during the day, or you set up something clever so they supply the supplemental light without blocking the sun.