The speaker describes something odd about his daily routine: he acts like a detective, keeping watch over a statue. The statue seems to have been put there as a replacement, a kind of stand-in, after he "fell" into other things. The poem's last line turns those things into a slide: writing, then "to morrow," then bed. Splitting "tomorrow" into two words makes it feel like a place he drifts toward, or keeps putting things off until.
The title, "Stunt Double," suggests the statue stands in for the speaker, taking his place while he gets on with writing and sleeping. Judging by the imagery, he may be thinking about how a writer's life leaves a stiff, still version of himself out in the world, one he feels oddly responsible for.
The mood is wry and quietly puzzled. The speaker sounds amused rather than upset, observing his own strange habit with a shrug. The tone is light, but there's a small unease underneath about what it means to be replaced.