i would just time both the lights to come on at once, for about 9-11 hours. youll have to watch your tank close for algae or of your plants start to close up after the light has been on for 10 hours or so, theyll let you know when theyve had too much light.
as for that 12000k bulb i personally think that is way too much on the kelvin scale, im pretty sure plants do best in the 6-8k range. I have 4 6700k bulbs and they work great. Lighting at least to me is a tricky game (especially in a bigger tank), too much and you get problems, not enough and no plant growth. You have about 3.2 wpg if you go with 240 watts, thats a lot of light without c02 and ferts. Its a hard game to play at first but try different things, youll be able to tell pretty quick what works and what doesnt. I am at about 2.1-2.2 wpg and running light c02, i have a small algae problem but i think its because i dont have enought plants to use the nutrients in the tank. you should consider c02 if you are running that much light IMO.
Good Luck