The front is blinking twice as fast because only one light is working. It's a safety feature of the blinker so you can easily tell when a bulb burns out. Once you get the other one working it will be fine.
A test light should be all you need, especially if it's one of the nice pointy screwdriver types you can poke into wires with. You can start by testing in the socket, then try socket hot with chassis ground, then move up along the wire towards the front of the bike until you get juice.
It's good to take the signal housing apart and look there, maybe pull the main tail light housing and look in there too. If you replaced the bulb and it's still not working a connection may have come loose somewhere. Check for a loose connector near the steering tube. They come apart here often since the bars are always moving back and forth. There's also a pinch point under the back left part of the fuel tank where a gold mounting bracket crosses the wiring loom. Check that.
If none of those solve it get a soild chassis ground with your test light and start working along the wiring loom from front to back until you find the place where you lose electricity.
Good luck!
Scott