Hmmm. Never even lived in a house with basement. Here's what helps me.
50pint dehuey in my 4x8x8 (I have the floor space luckily)
Day and Night, I vent the tent based on temperature, not RH. (or sealed running wall banger AC - AC keeps tent cool lights on. Vent during lights off)
15 minutes before lights out, a timer turns on my dehuey, preset to 40%.
The dehuey creates heat as it dehumidifies....so it vents as needed based on temp I set.
At the cost of energy, it works for for me.
Is it your basement that is always high RH.....outside air high RH also?
Basement humidity isnt the issue really except for summer.
In the winter basement temps are 65 f near constant with very low humidity. If i run the exhaust full time, temps are 65 in the tent
In the summer temps are around 70 to 75 with the water heater, laundry etc down there but humidity is around 50.
Tent i can try to keep stable, but at lights out humidity spikes if im exhausting based on temp, or gets too low if i exhaust on humidity.
I use led, so i know i should be keeping temps in the low to mid 80's, but that really isnt realistic with the amount of transpiration that goes on with temps that high.
I could try a dehumidifier this time of year, but in the winter it really wouldnt solve anything.