You have to remember that it can be hard to introduce male degus to one another as they can be very stubborn and very territorial over their space but it can be done with time, patience and a lot of effort. I have successfully done it twice now myself but i have only ever introduced one degu at a time to one another so it was a little different as not as much conflict to consider. The first thing to think of is remembering Rum and Raisin come as a unit and Jerry is an outsider to them so they might not accept him to start of with or at all as he's another dominant male and if theres already a leader in there it could cause friction, which is probably whats resulted in the fights so far. But it is worth having a go at introducing them as degu's do like company and you have nothing to lose
For a start you are doing the right thing at the moment by seperating the cage in two so they are next to each other and they can hear, see and smell each other. To add to that i'd also keep swapping the sides they are on so they pick each others smells up so they start to smell like one another, i'd swap them over once a week for a few weeks. I'd also make them share the same sandbath as well so they again pick some scent up of each other. Do you introduce them in the cage or in a neutral territory? The reason i ask is they might get on better if introduced in a neutral area as both will see the cage as their own territory so that could cause friction between them too so if you are using the cage i'd try using something or somewhere else where neithers scent should be present and if you do get them all together make sure the cage is clean so they have a fresh start together!
The good signs are the low whistling/chattering noise that you hear them make to one another like Rum and Raisin do, if they are doing that to Jerry as well thats a good sign as they are communicating with him and also if they accept him without any signs of aggression and let him groom them or vice versa as this is a bonding experience to them so an important step. The bad signs tend to be aggressive teeth chattering which is loud and rapid also tail banging and high pitched screeching and grunting tend to be signs of aggression and dominence, they are saying "this is my territory get out" or "keep away i'll bite if you come any closer". Remember that theres always going to be some territorial fights to start of with especially with a trio but they should only be minor fights to see whose going to be the boss and should sort themselves out within a few minutes but if they are more serious fights such as ones were fur and blood are flying and they continue to happen at every introduction then i'd probably keep them parted and living as they are. Degu fights can turn pretty nasty very quickly and sometimes over nothing and degu's have nasty bites unfortunately and can cause serious injuries to one another so if they continue to fight like this i'd keep them parted. If they can't live together in a group its not the end of the world as sometimes male degus do prefer to live alone as they like their own territory. If that happens then i'd just keep them as they are living next to each other so they can see and smell each other etc.... and give Jerry lots more cuddles and he should be perfectly fine and happy on his own!