What's the battery voltage key OFF?
Just after startup Voltage regulator will use +2volts, so 12.8v battery would see 14.8volt
After a few minutes voltage regulator should drop it down to +1volt, so 13.8volt
There is not an actual "number" the voltage regulator uses "push back" voltage/AMPs
Just after starting, the battery is drained so low "push back"
As battery gets recharged "push back" goes up so voltage regulator lowers voltage, actually AMPs, but in this case you measure the voltage
When you turn on all the lights "push back" in the system drops a bit so voltage regulator increases the AMPs, so you would see a voltage drop and then voltage would come back up once the lights were on, so AMPs were increased to match system "push back"
The Yellow wire on voltage regulator reads the "push back" in the system, I would test that it reads EXACTLY battery voltage with Key OFF
If it reads a little less then there is corrosion in that wire or at is connection to battery, which can be a fuse or fusible link
The corrosion cause low "push back" all the time so higher voltage all the time, which is bad for the battery, but it makes the lights brighter, lol
You can do this test after engine has been running for at least 10min
Engine on
Lights off
Heater fan off or Low
Test battery voltage, lets say it is 14.2volts
Turn on all the lights, turn fan to HIGH
test battery volts
Should still be 14.2volts
If its lower, like 13.9volts then voltage regulator is "stuck", its not adjusting voltage/amp output to the system