Definately sounds like low voltage..........
Check that with all the heavy-current stuff on ( HRW, A/C, headlights, heater blower etc, etc) there is still more than 12Volts at tickover.
If you haven't got a meter, treat yourself to one, it's the cheapest/most useful tool this side of a spanner.........
When turning at anything above tickover you should have a good 13-14V. Any less, the voltage regulator needs looking at.
It may not have been changed with the Alternator, depending on the design, it may be remotely mounted.
'73 Jensen Interceptor (Resting)
Giant Full Sus Mountain Bike