For anyone who is interested, here is the reply I received to my query to Midlothian council.
The recent closure and ongoing works using traffic signals was for the water main to be upgraded by Scottish Water
The current closure is for them to connect this new main to the system at the junction of Belwood Road and the A701.
As the excavation is in the middle of the junction there was no option but to close the road.
The gas main is on the opposite side of the road, in any case, which means any combined works would shut the road in its entirety.
These days all road works are coordinated through the Scottish Road Works Register.
The contractor will be away by Friday at the latest."
Fear knocks at the door, knowledge answers and finds nothing.