Funny you should ask about the carb sync, and the homemade tool. I just got back from test riding my BMW R850R after doing just that. In the case of the Beemer it's a throttle body sync, not a carb sync, since it's fuel injected, but the procedure is exactly the same.
Point 1: Carbs don't get out of sync due to slippage of a mechanical linkage. What you are synchronizing (equalizing would be a better word) is the vacuum in the carb bodies. This makes sure that the cylinders are pulling in the same amount of fuel/air mixture. This draw can get out of sync if there is unequal compression, the valves aren't quite equal, or if something in a carb has changed. A good carb sync will make a bike run smoother. Or, to put it more strongly, if they are not synced, it will make for increased vibration, and if it's bad enough, it can make the bike run badly. Some bikes are more sensitive to this than others. The Beemer is super sensitive to it, and runs like shit if the throttle bodies get out of sync.
Point 2: Make sure your bike even has two carbs. Not all V-twins do. If there's only one carb feeding both cylinders, there's nothing to sync.
The homemade tool: About 18 feet or a bit less of clear, flexible plastic tubing, 1/8" inside diameter usually. Whatever fits the vacuum fittings on your carbs. You may need a service manual to find the vacuum fittings on the carbs. They're generally in the form of small brass tube like things sticking out of the carbs somewhere, plugged either by covers that slip on, or by a rubber tube that connects the two together. Or, if you have a vacuum operated fuel valve, one fitting might be plugged and the other connected to the fuel valve. Anyway, about 18 feet of clear plastic tubing that slips firmly onto the vacuum fittings. Find the middle. Bend the middle over some kind of stick or board or something, but don't let it kink. I nailed about half an inch of the end of an old frozen orange juice tube with the metal end still on, near the end of a board and bent the tubing around that, and then ran each side up to the other end of the board and attached them. So you have a U shaped length of tubing, each side about three feet long, running the length of a 3 foot board. Some people actually use a yardstick. So now you've used 6 feet of the tubing, with equal 6 foot ends coming from the top of the board. Find someplace where you can hang this whole thing by the free ends of the tubing. Pour a small amount of 2 cycle oil into one end. Enough so that, when it all runs down into the U shaped end you have 6 inches or so coming up either side of the tubing. Pour little bits in at a time, as it takes quite a while to run down into the end. Wait till the inside of the tubing is clear each time you add some before adding any more. Go slow and take your time with this. It's a lot easier to add more than to run it out one end if you get too much in. That's it. You're done.
On most bikes, you need to remove the tank to get at the carbs, the vacuum fittings, the adjusting screw, etc. Once you've removed the tank, you'll need a long piece of tubing to use as fuel line to connect the tank to the carb. And, of course, the tank will have to be on something higher than the bike. If the fuel valve is vacuum operated, you will need to turn the fuel valve to "PRIME". If there is a "PRIME" position on the fuel valve, it is vacuum operated, so turn it to "PRIME".
To use your tool, hang it above the bike somehow with the U shaped end with the oil in it at the bottom. Keep the plastic tubing away from the hot pipes. Don't ask me how I know this. Attach each free end of the tubing to one of the vacuum fittings. There's one on each of the carbs. Do this with the bike off. Start the bike, but be ready to turn it off very quickly. If the carbs are really badly out of sync, one will suck the oil right into the carb. That's why you use two cycle oil - it's not the end of the world if that happens. If you're quick on the kill switch you'll catch it before that happens. Usually carbs are not that far out of whack, and all you'll see is the oil being pulled up one side of the tubing and, thus, down the other side. Just like if you sucked on one end yourself. Then you find the screw that adjusts the carb synchronization, and turn it one way or the other till the oil in each side of the tubing is about the same height. If possible, and it isn't always possible, you want the carbs balanced at idle, and at an engine speed that is in the useful power band somewhere. Not rocket science, but if you can get it balanced at a couple of points, that's better than just at idle. If the bike is air cooled, don't take all day doing this, as it will overheat just sitting still running. If it's liquid cooled that's not a problem.
Don't forget to cover the vacuum fittings back to whatever configuration everything was in.
This whole procedure is best done after a valve clearance check/adjustment. If the valves are way off, that could be the problem, and syncing the carbs to match would just be putting a Bandaid on it. Conversely, you should always do a carb sync after a valve clearance adjustment, since changing the valves will likely throw the carbs out of sync. They are both usually considered part of a routine tune-up.
