The R/R should have 6 connections, three go to the yellow stator wires in any order, thats the power input.
There will be a 12v (nominal) out and a ground. Get these connected as close as you can to the battery with as few joints in the way as possible.
Then there is a "sense" connection, this provides the feedback on the actual voltage in the system. On a stock bike this takes a long journey that can have voltage drops due to poor connections. Make this connection as close as you can to the battery + terminal if not actually on it.
For a lead acid battery "The actual resting voltage, or the voltage a battery will settle at 12-24 hours after being removed from the charger, is closer to 2.1 volts per cell, or about 6.4 volts for a 6v battery, and 12.7 volts for a 12v battery. These numbers assume 100% healthy cells, and may vary a bit lower for older batteries."
So your 13v is not enough to charge the battery, you need to see 14.5v or better.
'99 Vulcan "Victoria"