slowly climb back to 12.7 then turned switch off volt meter went back to 13.7
**Very important question**
Are you are reading ALL these voltages (13.70 V,,, 12.70 V,,, 3.80 V) DIRECTLY at the Battery POSTS and NOT at a fuse or some other point (engine block & fuse) or between the starter and engine block?
If you are reading these voltages DIRECTLY AT THE BATTERY POSTS,, using a HANDHELD multimeter (not any built in gauge on your bike),,, your problem (or at least 1 of them) is a bad battery.
If you are reading these voltages off some fuse, the starter or the engine block, Stop & back up. The battery may not be at fault.
You can take a perfectly good fully charged battery and pull it down to 3.80 volts using a 500 amp load. But the battery post voltage would never float back up to 13.70 volts when the load was removed. That is impossible. If the battery was good, the voltage would float back up to something like 12.25 or there about.
The nominal voltage PER CELL of a lead/acid glass mat battery is 2.1 volts. Therefore the nominal voltage at the battery should never exceed ~12.6 to 12.7 AFTER you take off the surface charge from the plates. In order to pull a good fully charged battery to 4 volts would require a huge load which in turn would strip the surface charge right off the battery.
I am also assuming that you are Not using some cobalt-ion or lithium-ion battery that has a nominal cell voltage of something other than 2.1 volts. Please don't tell me you have a Toyota Prius battery in your bike as an experiment.