Hi @Toriyama ,
I'm glad to hear you solve the problem ,if you have any issue about SharePoint, you are welcome to raise a ticket in this forum.
By the way, since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others." and according to the scenario introduced here: Answering your own questions on Microsoft Q&A, I would make a brief summary of this thread:
Issue Symptom:
"The underlying connection was closed: Could not establish trust relationship for the SSL/TLS secure channel" and "The remote certificate is invalid according to the validation procedure" on just 1 server
Solution:
- The API needs to go to some service, website. Enter this and click on the url and go to the certificate that is an option in the browser. You can download.
- Enter the server with error and import this certificate into the server's certificates.
You could click the "Accept Answer" button for this summary to close this thread, and this can make it easier for other community member's to see the useful information when reading this thread. Thanks for your understanding!