Actually. I think the term "glory hunter" is exclusively termed for the individuals that tend to interchange the football institution they support, based on the success rate of the club in context.

Where as, its a natural phenomenon when a neutral individual begins to support a team when the club is on a high. When the Club hits a low point in its history, as with all clubs do, that trend in motion then separates the genuine supporters from the glory hunters.

I cant use myself as an example because i began supporting the team i love back in '98 when Arsenal won the 97/98 season and it was so called the end of the Man United era. Coincidentally that 98/99 season, we won the treble, and in the following seasons we were doing absolutely phenomenal up to the point that the neutrals began despising us.
But almost immediately, our style ran out and with all the new changes into the squad and the news that SAF was going to leave us, our performances were affected and we began to dwindle. Then came the emergence of the reinvigorated Chelsea FC and the rest is history.

My point being, in those 3 season that we werent doing well, we got kicked out of CL pretty early, and our playing style was incoherent... i still supported my team.
Though i started supporting my team in the 98/99 season, i stood with my team until this very moment, and im helluva proud of them !!! So i refused to be categorised as a glory hunter... cos im not!

Im sure alota Scousers here are genuine liverpool fans, and its difficult to not admire you guys in general. Maybe thats why the rivalry is intensed between us, cos we're both really passionate supporters !

juz my 2 cents