Just like that....

[Bogertophis]

If temperatures are cool enough (like on the floor?) he may well "decide" to brumate...and he could literally turn up months from now. Snakes are actually
drawn to fresh outside air coming into our houses, so little gaps around plumbing (bathrooms or kitchen) can entice them to hide in a wall, or beyond. The
most dangerous place for a snake is our kitchen: snakes get up inside stoves, refrigerator motors-!, the underside of dishwashers, washers, dryers...AND
many of our kitchen cupboards have a crawl space under the bottom of the cupboards, and gaps are left underneath the cabinet front doors that snakes see &
head right up into that space...I know of no way to get a snake out of such a space short of ripping out cupboards, and doing so could hurt the snake.

I once had an 5' adult bull snake get loose and that's where she went...she got loose in mid-November & it took until mid-May before she was sliding across my
kitchen floor one night, finally ready for food. I had searched to no avail when she got out, of course, and I had no idea that's where she was but I suspected,
by process of elimination. She was fine, "none the worse for wear" & I was hugely relieved to have her back. Snakes really know how to "torture" us. My bull
snake was a good size though, whereas your little TP will quickly dehydrate by home heat, so leave some bowls of water around. But they also climb quite well
and can SMELL water, so your sinks, drains, toilets & even garbage disposal could end up attracting him for the moisture...I'd advise you to keep them covered
& checked on a regular basis. Snakes HAVE been known to get into plumbing...it's not pretty. (I have a hunch that my bull snake came out at night a few times
& got a drink of water from dishes left soaking in the sink...but of course, she would never say for sure...)

I do hope that your cat has not found your snake...that is sadly a distinct possibility also. I would also not advise using double-sided tape...that's too much like
a glue trap, which are horrible on small reptiles, not to mention the struggle which would attract your cat.

Keeping my fingers crossed for you for his safe & healthy return.