Predators are opportunistic. Yes, a fox usually lays low during the day but it isnt uncommon to see them out & about then either. Especially when there is an easy meal close by.
As far as the motion detector, it will scare them off the first or second time. After that they'll learn that the light presents no danger and continue to come back.
I had a fox on my game camera a few years back. Two pics were taken a few seconds apart, the third pic was no fox. Point being is the flash startled the fox in the first pic, the second pic three second later showed the fox turning to run, and three second later it was gone. I caught that fox in a trap two nights later and its mate the day after that.
Dont waste your time, effort, or money on a motion light, thinking it will deter predators.
Also, you wont catch a fox in a live trap, so save your money there too. A pup, maybe, but not an adult.
I'm not advocating trapping or killing the fox. I'm just sharing some info.