Time and Interval Based Power Up and Down

Looking to see if I can set up the Power HAT to power up at a specified time of day, then run an interval of power down and power up, until powering down for the rest of the day. And doing it the next day.

I am looking at powering a time-lapse set up with interval shooting and only need the RPi powered up for 3-4 minutes while taking the picture and transferring to a server.

I am currently testing it out now but wanted to know if the time function overrides the interval function. So I don’t run intervals through the night when not charging the battery pack over solar.

If there is a way to make this happen it would be greatly appreciated. Thanks!