I often noticed that ginger is included in much of the jamu recipes shared on the internet but it was not listed (by name) as part of the eight primary concoctions. Instead, ginger appears to be an add-on ingredient, except probably for jahe wangi or jahe rempah.
An invitation to share about the tea culture of the Malay community in Singapore led me to explore more about the Javanese wedang (hot beverage). In Singapore, the Javanese community is classified and managed as part of the Malay community.

Wedang is any hot beverage and in the Javanese community, the popular beverage are wedang jahe, wedang secang and wedang uwuh.
Ginger appears to be a common ingredient for most wedang and it could explain why it is not the main ingredient for any of the primary jamu concoctions – you are likely to consume ginger regularly as a beverage. In addition, ginger is commonly used in Javanese food.

Based on this observation, I make a distinction between the regular wedang as beverage and the jamu concoctions as supplements. In this classification, ginger (jahe/halia) is a primary ingredient for wedang but a secondary one for jamu, except probably for jahe wangi (which could also be called wedang jahe).