I've had an issue with my T500 with not being able to get the hose that goes between the air filter box and the carbs to locate properly and I've never managed to get a good seal at the bottom of the airbox.
In a recent VJMC magazine there was an article on T500 airboxes and the connection hose which explained that Suzuki had made changes to the hose over the years between T500 models.
I could see from the photos in the article that I had a early model type hose from the T500J or earlier, where as my bike is a T500M so should have a later hose designed for the T500K onwards.
The hose part is readily available so I ordered one from Legend motorcycles.
Here are the two hoses side by side , the new type that should be fitted to my bike is on the right. Note that the connections to the carb are further back, this is due to different carb mounting set up on the later bikes resulting in the carb inlet sitting a little further back on the back.
So I now have the correct hose but I found it still didn't fit. On investigation I found that the airbox I have fitted to the bike is the earlier type, the hose connection outlet is bigger and sits further forward.
The later air filter box is no longer available new so I need to either find one at an autojumble or ebay etc or modify my one to have a smaller outlet connection in a further back position.
As this will take a while I decided to buy a couple of cheap power flow airfilters (similar to K&Ns) which fit directly on to the rear of the carbs. I installed them and removed the old airbox completely.
I just tried the bike and it runs so much better with the new filters, it ticks over more smoothly and revs more cleanly so I may well stick with them for a while!