Paul__B:
The reason for using the DS3231 - in a module already built - is that it has a lithium battery backup which will keep it running during power outages - up to a year if correctly operated.Basically, that immediately trumps matters of cost and so-called "simplicity; in fact, the DS3231 is if anything, simpler, it contains the power changeover circuit - and the crystal - in one chip.
It is not "overkill" - it is the simpler solution.
If you want to frig around with other bits and pieces, well, go ahead, but if you actually want to get the job done, use the proper equipment.
so you would recommend DS3231+attiny?
Or there is a way to program DS SQW output to give 8 hours high 16 hours low output on its own (without micro-controller) I must say this would be the most elegant solution. Only DS3231 and relay...but is it possible?