So some ideas for dashed lines are found here - Tableau Tip Tuesday: Two Methods for Creating Dashed Lines
and here is another more elaborate method - Quick tip : Creating your own dashed line styles in Tableau | Bora Beran
In this case, I would address the need for a dashed line and what it is supposed to convey to the user of the viz. If it's really necessary to split it like you are asking, then maybe a dashboard with two different views - one with lines and the other with dashed lines would and then lining them up next to each other in the view to provide the sort of view desired. There is another problem though - the lack of data for all of those missing years means there is no data point to use for dropping a shape on the field for each year. Depending on the data, you may need to add in data to accomplish this.
I might go back to the start though to decide if a dashed line is the best answer or if other methods could be used to convey the meaning to the audience.