Have refilled HP cartridges for 20 years.
AFAIK, HP cartridges as old as yours don't have a time trigger but when the cartridge is totally empty there is a mechanical trigger to the tell the printer. Tri-color are the worst since when one color is gone, you got nothing.
- Run (or clean) the cartridge at least once a month minimum. When the nozzles dry out they are toast.
- If possible, don't wait until the cartridge is totally empty. It causes an alert. At the first sign of less quality refill them. Again, if you run them till no ink is left they are toast.
- Don't buy extra cartridges. They will dry out just sitting in the box brand new.
- As of lately, I don't use enough ink to fool with refill so I just keep the ones in the printer clean and buy refilled online for cheap.