Is it illegal to visit the Philippines for a few hours for a visa run? If so, how can I know in which SE Asian countries it would be okay?

Let's start by getting the terminology straight here. A "visa run" is when you work around visa length limits by leaving the country when one visa's time is up, and return immediately afterwards to reset the clock. These are at best in a grey area, sometimes straight up illegal as in Thailand, although as always enforcement varies, and the border official may well have been referring to this.

However, you're not asking about the country you are visa running from, you're asking about "to" side, which boils down to whether it's permitted to travel somewhere for a very short amount of time. And the answer is... yes? I've done multiple day-trips to Malaysia and Indonesia, including writing "day trip" on my landing card for the address, and I've never had a problem. The shortest of these trips was around 3 hours on the ground, since I met my customer at the airport!

What likely got you in trouble was confessing that you were visa running, which as noted is often illegal and always frowned upon, and thus makes you look suspicious to the other side as well. If you had worn business attire (collared shirt and pants) and answered "business meeting", I doubt this would have been an issue at all.

@jcaron's comment was quite helpful and provided the final "Aha!" moment for me. It links to the Republic of the Philippines Department of Foreign Affairs page list of countries for 21 day visa which says:

Guidelines on the Entry of Temporary Visitors to the Philippines:

Nationals from countries listed below who are traveling to the Philippines for business and tourism purposes are allowed to enter the Philippines without visas for a stay not exceeding thirty (30) days, provided they hold valid tickets for their return journey to port of origin or next port of destination and their passports valid for a period of at least six (6) months beyond the contemplated period of stay.

The issue had nothing to do with Taiwan or the "visa run" issues, it's simply because this time I did not have enough time to stay for a few days and enjoy myself.

With my departure time so soon after arrival it was pretty clear that I wasn't using my travel to the Philippines for "business and tourism purposes". While the person who booked my ticket correctly found a place I could enter without applying for a visa first, they did not read the "fine print".

When the agent at the airport said it was "illegal" this might or might not been exactly the most accurate adjective, it seems that the point is the visa is free because they expect you to go have fun and spend money or do business or both, and I wasn't doing that.

While @lambshaanxy's answer is informative, I've made an answer out of jcaron's comment because this really answers my question.

I have done a visa run from Taiwan to Manila in the Philippines that was 9 hours long and hit upon a similar issue.

When you enter the Philippines on a visa free entry they will give you a landing visa stamp and let you out of the airport. when I arrived they wouldn't give me this stamp and I was faced with a very long wait in the passport control area until my flight back.

They took me to the side where I waited with 1 or 2 other passengers from the same flight at a desk, while I filled out a form, this form was then taken away with my passport without explanation and returned to me 45 minutes later with a landing visa and i was told "You can go". I then left the airport and took a bus in to Manila.

If I ever have to do this again, how can I know ahead of time for which Southeast Asian countries this will be okay? Is there a list or specific search term by which I can find reliable current information?

In the before times, at least from Taiwan, I used to do visa runs of a few days to Ho Chi Minh, Bangkok or Hong Kong with no problems at all, I've heard people go to Okinawa too with no issues just remember to have a home made doctored .pdf of a "return flight booking" to show the check in desk at the various airports when returning to the country you are visa running from.

In these extraordinary covid times the situation is unclear in the hypothetical situation that Taiwan opened for visa free entry tomorrow:

Mongolia and Laos seem like the most open countries nearby, but with no direct flights from Taipei to either of those destinations they would not be practical for visa runs.