mine was so old it had a capacitor looking thing in the system.. it was 25y plus stuff. no idea how to replace it end up replacing with the housing. the end part dried and cracked anyways

Forget about the capacitor. The capacitor is for suppress the noise from the florescent light. Also called EMI capacitor. It is under safety class capacitor. It is designed to open circuit when failed. Traditional circuitry is more conservative and new design is to reduce cost 

For LED, it is not needed since you do not have starter that create spark, thus noise.

Reverse polarity.

Ok, I was wrong here. It is for power factor. The EMI capacitor is built inside the starter already.

I believe in olden days, the florescent light set did come with capacitor inside. However, improving power factor does not contribute to any saving on your electricity bill since you are charged for power usage only as recorded by meter in kWh.  Household are not charged for power factor in billing.