Not sure what remote socket the DSC HX400V camera has. I have the DSC RX10M4 and use a Pixel Pro TW-283 intervalometer with a Pixel DC3.5-S2 Off Camera Shutter Connecting Cable which I think is standard for all Sony Cyber Shot cameras. Can't fault the set-up.
This is wired or wireless with a small receiver that sits in the camera hot shoe when needed.
