Many pilots struggle to properly use an HSI when flying a localizer. If you’re inbound to a VOR on a given course, pass the station and proceed outbound, you don’t change the OBS, right? Likewise, when outbound on a localizer, don’t change the OBS, HSI or not. So, similarly, if you’re flying the front course—inbound or past the runway—you select the front course by convention for situational awareness, even though a localizer doesn’t care where the OBS is.
Flying a localizer back course is where it gets interesting. On that conventional VOR/LOC indicator, you (should) still dial up the front course under the OBS. Then, you’d correct by turning away from the deviation needle. On autopilot, you’ve got to select reverse sensing, usually with a “back course” mode. So far so good.
You do exactly the same thing with the HSI. Consider a Localizer Back Course Runway 36 approach. Set the HSI course selector to 180 degrees (front course), but your heading on final is 360 degrees. You’d normally turn away from the CDI to correct, but since the CDI display is turned upside-down, where a normally-right deflection is to your left—automatic reverse sensing—just steer toward the depicted CDI. You still use back course mode on the autopilot, though.
Note: Some autopilots also want the heading bug set appropriately.