Try turning tank lights off and sitting some distance from the tank during the day, or room lights off and again sitting away from the tank at night. You'd need to give them time to start ignoring you and going about their business. If you have two parrots and two jewel fish, one of these may be pairing up and causing trouble. Or you could simply have a single troublemaker. Some jewel fish are troublemakers, I've seen them attack much larger fish, they can make a mess of another fish quick if they want to.
Which type of parrot cichlid? the man made fish-- see
link, or the natural species, Hoplarchus psittacus-- see
link
How to know if GT are courting-- 'courting' is what people call the ritual in which they pair up and prepare to spawn-- for GTs it's similar to a lot of other cichlids. To start with both fish generally pick and focus on a sport in the tank, where they'll hang out together. They may do some housekeeping, clearing debris away from the site, etc. Aside from that they focus on each other with behaviors that can include: repeated head shaking, one or both turn their sides to the other and flare fins or gills, circling, tail slapping, wrestling matches with their lips locked.
Some of this can resemble fighting but it's more ritual than actual fight, at least in GTs, the intent is to size each other up, not injure, one doesn't chase the other all over the tank, etc. --except in some cases where one wants to breed and the other isn't ready or interested.