If you fast travel, log off, or leave the planet, the quest timer will start when you return, but you WILL NEVER GET INFECTED. Just abandon the quest, pick it back up and get in a fight with a strong / elite ghoul. It will update instantly. Good luck.
Sorry for the necro.
No, necro good in this case
After being infected about two dozen times with no quest update this had me so frustrated that I logged off and haven't played my GS in a week. I'll have to try this later today (I did in fact abandon the quest before the rage quit).