What are a marker's duties during a singles game?

Bowls Australia describes the marker's role as assisting players to make sure the game proceeds within the established laws. A marker prepares for the game and gathers the required equipment, then positions themselves, demonstrates on the green and makes assessments during play, and completes the scorecard after the game.

Under law 42 of the Laws of the Sport of Bowls (Crystal Mark Fourth Edition), the marker must:

• check the mat is on the centre line, centre the jack and check it is at least 23 metres from the mat line;
• stand to one side of the rink, behind the jack and away from the head;
• answer the player in possession of the rink about the state of the head, the position of the jack and which bowl or bowls are shot;
• mark touchers with chalk and mark touchers and the jack in the ditch;
• stop bowls from neighbouring rinks that could move a jack or bowl at rest;
• not move the jack or any bowls until the players have agreed the shots;
• measure disputed shots when asked, and ask the umpire if the players are not satisfied; and
• record the score after each end and complete the score card at the end of the game.

In the absence of an umpire, the marker must also make sure all aspects of play follow the laws.

Sources: https://bowls.com.au/get-involved/officiating-laws/marker/ and https://www.worldbowls.com/laws-of-the-sport/