The dealership might be right. This happens with a lot of old cars when they're switched to synthetic. It happened to my old 97 Buick Park Ave, but those are already prone to leaks. It did not happen to either of my old Jeep Cherokees, a 96 & 99, but those are less prone to leaks. However, the old Cherokees did experience lower oil pressure with 5w30 and 10w30 full syn, which was not an issue with conventional 5w30 or 10w30. I then tried 5w40 full syn in the Cherokees and then oil pressure was back to normal.
The safest course of action is to continue using the same oil your dad used. You know ot works. Why spend extra money to roll the dice on full synthetic? Your car doesn't need full synthetic.
Every mechanic who I personally know recommends against switching an old car to full synthetic, or at least advises customer of the risk. Why risk it?
Think of it as a bet.
If you win the bet, you get to spend extra money on expensive oil that you don't need. That extra expense will be ongoing and synthetic won't be on sale most times.
If you lose the bet, you have an oil leak or low oil pressure. Maybe both.
The bet is all risk, no reward. I suggest listen to the dealership on this issue.