This is very common and I have never seen anyone post a solution to the problem. I've been looking for a few years. It's related to the slot reels -- when plugged in, f116 will heat up until it's extremely hot to the touch and ultimately blows. Try unplugging the blue connectors that go directly to the reel stepper motors from the stepper motor driver boards and see if the fuse stays cool. I bet it will.
In my case, I operate a Whodunnit on location, and after spending weeks trying to solve the issue before putting it out, I ended up simply leaving the reels disconnected. It's a bummer to lose the moving reels, and I'd love to find an actual fix, but it did make the problem go away. Some of the things I've tried in my quest to combat the issue (this was a couple of years ago so my memory is slightly fuzzy) include swapping driver boards and CPUs with known good ones, replacing all reel motors with brand new ones, methodically checking all wiring for shorts, swapping reel pcbs around with a known working game that didn't have the issue, and ultimately swapping in the entire set of pcbs, reels, and motors from another Whodunnit that doesn't get hot or blow its fuse -- on my machine it still blew the fuse. We swapped it back into my friend's game, and it didn't blow his fuse. So as far as I can tell, the problem isn't related to the reel motors or related pcbs. I should add that my friend is one of the smartest people I know, and one of the best techs, and he and I spent several hours on it and ended up stumped.
Here are some other threads about it, each without any kind of resolution:
https://pinside.com/pinball/forum/topic/whodunnit-error-check-fuses-f115-and-f116-j112-and-opto-12v-supply#post-3329415
https://pinside.com/pinball/forum/topic/check-fuses-f115-and-f116-j112-and-opto-12v-supply#post-3132562
https://pinside.com/pinball/forum/topic/who-dunnit-reel-steppers-repostupdate#post-850112
https://groups.google.com/forum/?hl=en#!searchin/rec.games.pinball/whodunnit$20f116|sort:relevance/rec.games.pinball/3QdXDejUW0k/G7vt6qGUzGAJ
https://groups.google.com/forum/?hl=en#!searchin/rec.games.pinball/whodunnit$20f116|sort:relevance/rec.games.pinball/0DETRqLIK9Q/ngrP7z0fVuIJ
https://groups.google.com/forum/?hl=en#!searchin/rec.games.pinball/whodunnit$20f116|sort:relevance/rec.games.pinball/sJAEWaFDdQg/NFU4TcDtxLkJ
I'm actually just about to shop out my Whodunnit again so I can put it back on location, so I'm once again super interested in figuring out an actual solution. It seems like everyone ends up stumped. I've talked to a couple of other operators who have the issue, and they tell me they just leave the reels disconnected, too. I'd love to avoid that this time around, but I really don't know what else to try. Hopefully some people with the problem will come out of the woodwork in this thread and we can put our heads together and figure this thing out once and for all!