Can my son extend his 30-day stamp if it expires on a public holiday?

I've been in a similar situation, and there was no problem. It depends on the office you use, and the individual serving you in most cases.

Yes, with no fine if he goes immediately on the 13th, since the office is closed for a holiday on the date his stamp expired.

He will get 30 added to his last expired day...

If he’s a youngster he can’t be fined for any overstay you don’t need to extend him

I assume your son's 30 day stamp is an entry stamp not an extension (as you cannot get 2 tourist extensions)

You can get a stamp up to a week before at immigration no need to wait for expiry date

If your son is eligible for a 30-day tourism extension, he can apply for one at the local immigration office. As the last day is on office closure, he will get the stamp that says the overstay fine is waived and he can get a tourism extension as normal.

Next time, don't wait until the last day for a tourism extension as it will be added to the entry stamp (top-up), no downside to doing it earlier.