So I found out how I need to approach this.
First the larger issue that is solved using the FME workbench is that we had line data from multiple sources that the needed to flatten into one set of lines with overlapping duplicate line areas removed.
This was then to be aligned with supplied point data and segmented on these points into smaller line segments.
To solve the question above we used TopologyBuilder transformer to digest all of the line data and get a new line set based on the generated topology. The workbench then uses the LineJoiner transformer to connect all of the end to end line segments together into longer lines ready to be segmented.
Analysis showed that this approach we were loosing <2% of the line data we were processing. Thos was through both the Topology generation and discard of invalid line segments from the line joiner.