I have an A7RV and I have done night time lapses. I just have a button set so I can turn the screen on and off. I don't have the problems you are describing. Maybe a full camera reset may help. I don't know.
It's worth noting that at least with this camera, during a nighttime timelapse the screen is grey all of the time. As the camera seems to lock up while capturing a frame and turn grey, I cannot review the last image or offload the image to an app. It's not uncommon to capture back to back images all night long, so the screen is forced to be on and grey all night with no option to review remotely. I have tried a series of apps that all appear to be Locked out of offloading images for review. Ideally I would have the option to review and tweak settings... but at the moment I cannot even review to identify if there is an issue. Physically touching/pausing the sequence would destroy it.