Leaking through the base of the stem means you have a punctured tube, that's just where the air can get out of the wheel as the spoke nuts are probably rusted airtight.
Get a good quality tube, Michelin or Pirelli are excellent. I've had poor experiences with no-name (China) tubes with wonky tire balance and bad valves.
I have patched tubes with hot vulcanizing patches (you clamp them on and light some stuff that burns a few seconds to melt the patch on) but I haven't seen them for years in stores. I don't trust glued patches on a motorcycle, flats are too frigging scary.
