Yes, I would get a volt meter and put it on the battery.
Good battery will be 12.3-12.8 volts
12.2 volts means battery can only hold 50% charge, lower is even less charge, batteries are usually at this voltage after 5 to 7 years of use, time for a new battery
Start engine
Battery should now read 14.6volts to 14.9volts, this is "recharge" voltage, it will last about 3 to 5 minutes, the newer the battery the less time it takes to recharge it.
After that it should drop down to 13.5-13.8volts, this is "maintenance" voltage, enough voltage to run the vehicle and keep battery charged but not "cook it"
Turn fan on to high, and turn on the head lights, voltage should drop then come back up to 13.5volts at least
If voltage drops down too low engine electrics start to "brown out", misfiring and stumbling
Alternators have 3 "Fields" that generate voltage, as they get older it is common for 1 field to fail, dimming head lights at idle is a sign of that, but 2 fields can run vehicle and keep battery charged as long as you are driving, above 1,500 RPM.
If a second field fails then there simply isn't enough voltage to go around