why is there no phone number I can call.

Because it's literally nature? There's no office or anything before entering, but you could probably look up the Jemez Springs wilderness control or something and find a number

There are no facilities there, or even a "hot springs" sign, the sign just says the trail closes at sunset, just a washed out road that takes 25 minutes driving 5 miles an hour.

This is a completely wild area. The road of about 4 miles is next to impossible to drive even with a jeep or SUV. Some locals might tell you how to find it. No clear trail their once you park either.