"Is there any way to test the voltage regulator"
My answer: YES there sure is (see my Test Procedure URL Link posted below)
Not being there and as a past used tractor dealer I can tell you manyyyyyyyyy many tractors got changed over or jury rigged etc so I cant say if you actually even have a full fledged Voltage Regulator as you call it or the original 2 wire (BAT/GEN) Cutout Relay that used the manual light switch Low/High charge control system.
In Para 5 of my Troubleshooting Procedure theres a test you can perform that tells if the Genny itself is the problem or else its the fault of the Voltage Regulator or manual Low/High light switch charge control system. Basically when shes running you dead ground the Gennys FLD post and if it charges then but NOT otherwise (says genny itself is okay), the problem is EITHER the Low/High light switch charge control HAS A BAD GROUND (its gotta be grounded well to work, a common cause of no charge),,,,,,,,or the wires bad or missing from FLD on genny to the Field connection terminal on the switch,,,,,,,or the Low/High switch is bad,,,,,,,,,,or if it has a VR as you mentioned its not well grounded or is bad.
Not running a good and charged up 6 volt battery should read around 6.3 volts BUT when running at fast RPM a good genny should raise the voltage to at least 6.5 up to 7 or so.
Make sure the belt is good and its tight,,,,,,,Make sure the Low/High switch has a good ground,,,,,,,,,Make sure theres a wire from FLD on Genny up to LH switch,,,,,,,,,If it has a VR make sure its well grounded,,,,,,,,,If no charge dead ground the gennys FLD post n see if she charges then when at fast RPM???? if so see the above and my Troubleshooting Procedure. If no charge even with FLD grounded and the VR or Cutout Relay by passed, the VR or LH is out of the equation so the genny must be bad. Also try my Genny Motor test to test just the genny