Emergency services were dispatched to the tower block just after 13:00 on Monday and nearby Dalmuir train station was closed, causing cancellations to trains.
ScotRail said the station had now reopened with services running as scheduled but warned services may be subject to delay, alteration or cancellation.
Police remain at the scene but BBC Scotland News understands the remaining cordon is likely to be lifted later on Tuesday morning.
The entrance to the block is now open with some residents already returning to their homes after spending the night in temporary accommodation.
Forensics officers have been in the area since the unexplained death of the 58-year-old man on 17 October.
Residents of the 15-storey block were told to leave their homes as quickly as possible on Monday after the suspect item was found and the area was cordoned off.
It is not known how many people have been evacuated. Police Scotland said there “was nothing to suggest” the suspect item was linked to the death.
The nearby Dalmuir community centre served as a rest centre with some residents spending the night in a hotel.
