In a Facebook post, the former Home Minister of Kerala referred to an activity of toddy tappers, implying the job performed by Vijayan's late father.
A trial run was conducted with a locomotive along a section of the new track on Friday evening.
Trains which have not been cancelled will conduct service along Alappuzha.
Pinarayi Vijayan on Thursday inaugurated the revamped Kerala Paper Products Limited at Velloor.
The place is located at an elevation of 4000 ft above sea level
The dead are Jibin Jose Mathew (29) of Akalakunnam in Kottayam district and Kiran V Shah (29) of Ernakulam.
The double track will be inaugurated this month
The incident happened on Sunday evening when he was all alone at his house. The youth slit his wrist in the video titled 'My suicide live'.
The popular doctor retired from government service in 1983 when he was the Assistant Professor at the Kottayam Medical College Hospital.
Meanwhile, water started receding on Wednesday after rain stopped.