The back up computer in your bc won't do much good without your spg unless you plan to immediately abort the dive. Why not just keep the spg hooked up and keep diving. I use AI wrist and back up wrist. Also have spg on a super short clipped to my plate, but still usable.
Computers do fail. I've had 3 failures in ~10 years. All 3 times I had back up depth and time device and continued the dives using tables. The last 2 times I made repetitive dives as well.
Actually that is my plan if I have a failure with my AI computer, to immediatly abort the dive. with lots of dives on the AI computer I actually don't have any worries about it and if it does happen I'm ok with that trade off of not having that extra piece I don't want to deal with (the extra spg). I did learn on a hose mounted spg, 1983 we actually only had oral inflate BCDs then too so I have seen the gambit of gear and like the new technology, and trust it, but not so much that I don't have a back up plan.