Small Engines (Lawn Mowers, etc.): HONDA HRB475SME K2 MOWER CHARGING PROBLEMS!, regulator rectifier, battery cables

Question
Good Morning,
I am having problems with a Honda HRB475 SME K2 serial no:MZAZ 8233010 ( GXV140 ENGINE ) Petrol Mower with electric start.
It has a battery charging problem. The output directly from the Charge coil is between around 16-17 volts AC. Then taking output directly from the combined regulator / Rectifier I find it is putting out only 5 volts DC  but also shows when on the AC scale with 3 volts ? Yet this is a new regulator /rectifier I have just put on and the old one I replaced gave the same readings. The regulator is 5 amp and is Honda part no 31750-735-013. The Charge Coil is Honda Part no: 31510-ZE2-H91.
I have also plugged the battery in and took a voltage reading while the engine should be charging the battery and it still says 5 volts?? The battery is now very low on charge at just over 12 volts.
I am quite baffled by this?
Can you help me in any way?

Answer
Is there any way you can wire the regulator directly to the battery?  It may be possible the key switch is causing the problem, not likely but possible.

Oh yeah, did you have the battery load tested?  Did you dis-connect the battery cables and clean the battery terminals and cable ends with a wirebrush?  I've fixed a lot of charging problems just by cleaning the connections.

Finally, pake sure all the grounds are clean.  Honda has had issues in the past with poor grounds.

Eric