I am searching for examples of both LRT and HRT single track (or significantly so) operations
A lot of LRT lines are built with substantial sections of single track, with the possibility to infill later. I know portions of the Baltimore and Portland systems were built that way. It pretty much limits you to headways no shorter than 10-15 minutes, so it's hardly worthwhile for most systems.
I don't know of any HRT systems with single track for any substantial section - only shuttles, terminal stations, etc. By the time you're spending the money for HRT, you're expecting high enough ridership that you're going to be running much more frequently than single track can support.