You have one of the early series TS185s that are more rare than the later reed-valve models, from 1977-78 on to the present (and how many cars/bikes have had a 30 year production run with only cosmetic changes?!!). I would suggest you keep an eye on eBay, or join the Vintage Japanese Motorcycle Club email list. To do this send an email to:
How big is the hole? It's amazing what you can fix with JB Weld.
Regarding the sticking float, it will be the float valve, unless the float is holed. The float can be re soldered as the early ones are brass. To check for holes, shake the float to see if the is any fluid inside. If it has fluid inside or you want to check another way, hold the float in hot water to see where the bubbles come out. Mark the place and use a hot solder gun to repair after wire brushing the area around the leak.
The float valve is either a metal on metal valve or a rubber tipped valve; I'm not sure which. The metal ones can often be refurbished using fine grinding paste and a very slow drill (I use a very old hand twist drill) to spin the valve.
Rubber ones can be softened by soaking in DOT5 synthetic brake fluid for several days. The same technique is also good for softening hard old carb and airbox boots.
Check to make sure someone has not tried to deal with the leak by bending the float tab up to make the valve seat more firmly. This will lower the float level and make the bike run lean. TS185s, like all two-smokes, rely on the vapourisation of the fuel to help cool the piston and running lean risks seizure.
If the bike has been sitting for a while often the fuel galleries will have fuel gum in them, blocking the idle and choke circuits. Simmering the dismantled carb in a 50/50 mix of Yamaha Carb Cleaner and water, outside please, over a little gas cooker, for 15-20 minutes will fix that. This is NOT how the instructions on the bottle tell you to do it, but it has returned furry lumps of aluminum oxide back to working carbs for me many times. Save the liquid as it can be reused dozens of times.
Another common problem with an old two-smoke that has been sitting is the crank seals get leaky. If the motor will only run with the choke on, it is pulling air in around the crank seals.
Email me directly off the HUBB for further instructions or help.
Nigel in NZ