SSL_SESSION_ID does not appear HTTP header in first access

Issue

We're trying to use the mod_ssl environment variable %{SSL_SESSION_ID}s and put it in the response headers. So we put the following line into our httpd configuration file:-

Header set SSL_SESSION_ID "%{SSL_SESSION_ID}s"

Also, according to ¹, we configured SSL session cache DB. However, I still can't consistently get the session ID in the headers. Empirically, it appears that SSL_SESSION_ID in the headers is null on the first access within the SSL session and it's only being put into the headers on the second call.