I suspect the reason you found only negative and not helpful answers is because the idea doesn't really make sense.
Uptime is kept track of in /proc/uptime it's read only, you cannot write to it. I think the closest you could get to what you want to do would be to replace the 'uptime' command with a simple script which outputs whatever value you want.
The time after which the reboot occurs is a symptom, not the cause. It's not going to be the case that some process says "Oh hey the system has been up for 12 hours and 39 minutes, I think I'll cause the system to crash and reboot now". Some condition is being reached once the system has been up for a certain time, like something runs out of memory. You can't fake that short of a time machine. Could it be a hardware problem? Maybe it's overheating and tripping some sort of inbuilt protection? How certain are you that the problem occurs at intervals of 12 hours and 39 minutes? (You say there are no logs, so how do you know how often the problem occurs?)