Search terms would include ¼" mono jack plug, 6.25mm 2-circuit jack or male connector.
TS or T-S doesn't work so well in google. Mono and stereo would really be 2 circuit or 3 circuit in a search, along with TS or TRS, but it's too complicated. If you are going to snake these cables all up and have the floor box able to be moved, you might be better to use a fairly heavy microphone cable, and fit a 3 circuit TRS (stereo headphone type) socket on the box and the male at the remote end - because then it could be used for other things if you needed them later - I'm thinking that it could be handy to remote a headphone output - that kind of thing. If you use a standard guitar amp 2 circuit system, you can't use headphone on that circuit - but if you use a 3 circuit version, you can do either. If your amp is loud, just make sure you use cable with sensible sized conductors.
I'm surprised your Google search didn't work - or are you trying to find a multicore cable that has these facilities? All down one cable?
If so - just remember that it's usually considered bad practice to squirt 100 odd Watts of audio down one core, and have a mic level signal coming back up another. Crosstalk between the two can produce some leakage, which isn't good. You can get the cable if you want to try it - search the usual suppliers but apart from some very expensive specialist ones, you won't find a mic and speaker core system - you need to look at the cable specs, and see if the cores are foil screened, with sensible size conductors - but I'm not sure if this is what you meant?
