Here's a perspective on what dive computers, bottom timers, and dive watches do for you.
As we learned in OW class, critical things we need to know for a dive are depth and elapsed dive time. We used these in class to plan our dives so as to avoid decompression obligations.
A dive computer keeps track of depth--including varying depth--and time, and it continuously updates one's remaining no-deco time. That's the computer's central function. It's a kind of automated dive table. Since it "knows" depth and time, it displays them in addition to remaining no-deco time.
A bottom timer "knows" depth and time, but it doesn't (can't) compute remaining no-deco time. Even so, if you enter the water having planned your dive, you'll have at least an idea of the dive's max depth and time, so a bottom timer can backup your computer if it dies (dead battery, flooding, lost, etc.). With your dive planning information and a bottom timer, you'll have a good idea of your situation regarding decompression. Some even carry dive tables with them so they can update their dive plan underwater, using the bottom timer's information.
A dive watch, unlike a bottom timer, is a waterproof time piece. As a watch, it doesn't know or display your depth. Therefore, it can't be used to back up the dive computer's key function: computing remaining no-deco time. [Exception: if you dive a square profile--go to a planned depth and stay there until you ascend--you already know your depth, so elapsed time is all you need to stay out of deco trouble, if you've planned your dive.]
So: If the question is how to back up a dive computer in case it fails, there are two options. One is a second computer! The other is a bottom timer and good dive planning (which you should do, anyway). A dive watch shouldn't be considered a backup: it will only give you time, and there's not much no-deco time insight to be gained from time alone.