The term "wagon" refers to the days when people used horse-drawn wagons to transport goods and people. In the 19th century, it was common for workers who were paid in cash at the end of the week to spend a significant amount of their earnings on alcohol, leading to drunkenness and absenteeism from work.
To address this issue, some employers implemented a system known as "payday on the wagon." Instead of paying workers in cash, they would give them tokens or scrip that could only be redeemed for goods at company-owned stores, where alcohol was not sold. This system encouraged workers to save their money and discouraged excessive drinking.
Over time, the phrase "to go on the wagon" came to be used more generally to refer to giving up alcohol or abstaining from drinking for a period.