Things that came in the box with the camcorder when new: Page 35. No wireless remote.
Did a search using "remote" in the pdf: 7 hits all associated with using the Sony TV's "Remote Commander" wireles remote to control the camcorder when connected to a Sony Bravia TV for playback only.
This camcorder has no capability to deal with a remote.
Most camcorders don't pause. Start/stop = file. To combine the files, get the captured video into a computer and edit with an AVCHD-capable video editor. Export/render the file...
Contrast this with camcorders that have remote capabilities:
This one uses a smartphone over wifi for the remote
(note: no pause)
This one comes with a wireless infrared remote:
The CX220 (or PJ220) does not have wifi and does not have an infrared receiver to use the Sony Remote Commander in the way you require.