Self-empathy seems to me to be a form of luminosity.

Since you're with yourself all of the time, I'd say it is useful pretty much all the time.

Edit: Wow, this was timely. Barking up the wrong tree just posted this:

Study after study shows that self-criticism is consistently associated with less motivation and worse self-control. It is also one of the single biggest predictors of depression, which drains both “I will” power and “I want” power. In contrast, self-compassion— being supportive and kind to yourself, especially in the face of stress and failure— is associated with more motivation and better self-control.

As a practical matter Theater has been shown to increase empathy for those on the Autism spectrum (hi!) so if you consider yourself particularly bad at empathy (also hi!) then I would personally recommend theater and improv.

http://www.sensetheatre.com/pdf/researcharticle.pdf