The latter type I still use today when I am on a long run and start to feel like I might fade toward the end. I have usually fallen into a rhythm where I am inhaling for two steps and exhaling for two steps by steps in a run. During that two step exhalation, I just add in breathy two-syllable words or phrases that I find sort of encouraging or motivational at the moment, and repeat them each time I exhale (sort of under my breath, so passersby aren't offended).
My favorite is to repeat "hell yeah" and "feels good" on alternate breaths.
hell yeah--------------feels good------------
This works for me. Somehow, it lifts the spirits just a little and offers enough psychological benefit that I can break through the mental barrier and either maintain or pick up my pace a bit in the last couple of miles. Maybe it's just something to focus on other than the fatigue, but all I have to say about the subject is...
Hell yeah! - - Feels good!